Borochkin A. A. International Finance. Lectures. Part 1

International Finance

c.econ.sc.Alexander Borochkin

Literature

The Foreign ExchangeMarket

International MonetaryArrangements

The Balance ofPayments (BoP)

Forward-looking MarketInstruments

Binomial OptionsPricing Model (BOPM)

1/ 126

International FinanceLectures


2018



LiteratureManualsLegislatureInternet resources






2/ 126

Manuals

Claessens S., Kose M. A., Laeven L., Valencia F.Financial Crises: Causes, Consequences, and PolicyResponses..Washington D.C.: Intl Monetary Fund, 2014. 635 pages.

Madura J.International Financial Management.USA: Cengage Learning, 2011. 736 pages.

Melvin M.International Money and FinanceOxford, Academic Press, 2012. 336 pages.

Shapiro A. C.Multinational Financial ManagementHoboken, New Jersey: Wiley, 2009. 784 pages.









3/ 126

Legislature

Federal Law «On currency regulation and currencycontrol» dated 10.12.2003 173-FZ (amended12.03.2014 33-FZ) // SPS Konsul’tantPljus. URL:http://www.consultant.ru.









4/ 126

Internet resources I

MetaTrader 4. Trading Platform.URL: http://www.metaquotes.net/ru.

Vedomosti [Electronic resource]: newspaper.URL: http://www.vedomosti.ru/.

Kommersant [Electronic resource]: newspaper.URL:http://www.kommersant.ru/daily/.

World Economy and International Relations[Electronic resource]: scientific journal.URL:http://www.imemo.ru.

Financial Times [Electronic resource]: newspaper.URL:http://www.ft.com/home/uk.









5/ 126

Internet resources II

New York Times [Electronic resource]: newspaper.URL:http://www.nytimes.com/.

Wall Street Journal [Electronic resource]:newspaper.URL:http://europe.wsj.com/home-page.

International Monetary Fund [Electronic resource]:official site.URL:http://www.imf.org/external/russian/index.htm.

World Bank [Electronic resource]: official site.URL:http://web.worldbank.org.

World Trade Organization [Electronic resource]:official site.URL:http://www.wto.org/.









6/ 126

Internet resources III

United Nations (UN) [Electronic resource]: officialsite.URL:http://www.unrussia.ru/public.html.

United Nations Industrial DevelopmentOrganization (UNIDO) [Electronic resource]:official site.URL:http://www.unido.org.



Literature

The Foreign ExchangeMarketForex definitionInternational MarketparticipantsFinancial centresCurrency quoteLong and shortpositionsCurrency ArbitrageShort-term andLong-term ForexMovementsRussian forex market





7/ 126

Content

1. The Foreign Exchange Market1.1 Forex definition1.2 International Market participants1.3 Financial centres1.4 Currency quote1.5 Long and short positions1.6 Currency Arbitrage1.7 Short-term and Long-term Forex Movements1.8 Russian forex market



Literature






7/ 126

Foreign Exchange Market definition

The foreign exchange market

is a place where large commercial banks tradeforeign-currency-denominated deposits with eachother. The foreign exchange market (forex, FX, orcurrency market) is a global decentralized market forthe trading of currencies. This includes all aspects ofbuying, selling and exchanging currencies at current ordetermined prices.

The modern foreign exchange market began formingduring the 1970s after three decades of governmentrestrictions on foreign exchange transactions.



Literature






8/ 126

The foreign exchange marketcharacteristics

huge trading volume representing the largestasset class in the world leading to high liquidity;geographical dispersion;continuous operation: 24 hours a day exceptweekends, i.e., trading from 22:00 GMT onSunday (Sydney) until 22:00 GMT Friday (NewYork);the variety of factors that affect exchange rates;the low margins of relative profit compared withother markets of fixed income;the use of leverage to enhance profit and lossmargins with respect to account size.



Literature






8/ 126





Literature






8/ 126





Literature






8/ 126





Literature






8/ 126





Literature






8/ 126





Literature






9/ 126

The size of the Forex market

Table 2.1: Global foreign exchange market turnover,daily averages in billions of US dollars and percentages

Instrument 1998 2001 2004 2007 2010 2013

Foreign exchangeinstruments

1527 1239 1934 3324 3971 5345

Spot transactions 37% 31% 33% 30% 37% 38%Outright forwards 8% 10% 11% 11% 12% 13%Foreign exchangeswaps

48% 53% 49% 52% 44% 42%

Currency swaps 1% 1% 1% 1% 1% 1%Options and otherproducts

6% 5% 6% 6% 5% 6%

Source: Bank for International Settlements. Triennial CentralBank Survey. Report on Global Foreign Exchange MarketActivity in 2013. Basel, December, 2013.



Literature






10/ 126

Table 2.2: Global foreign exchange market turnover by currency pair,daily averages in billions of US dollars and percentages

2001 2007 2013

USD / EUR 372 (30%) 892 (26,8%) 1289 (24,1%)USD / JPY 250 (20,2%) 438 (13,2%) 978 (18,3%)USD / GBP 129 (10,4%) 384 (11,6%) 472 (8,8%)USD / AUD 51 (4,1%) 185 (5,6%) 364 (6,8%)USD / CAD 54 (4,3%) 126 (3,8%) 200 (3,7%)USD / CHF 59 (4,8%) 151 (4,5%) 184 (3,4%)USD / OTH 199 (16%) 612 (18,4%) 213 (4%)EUR / JPY 36 (2,9%) 86 (2,6%) 147 (2,8%)EUR / GBP 27 (2,1%) 69 (2,1%) 102 (1,9%)EUR / CHF 13 (1,1%) 62 (1,9%) 71 (1,3%)EUR / OTH 20 (1,6%) 83 (2,5%) 52 (1%)

All pairs 1239 (100%) 3324 (100%) 5345 (100%)

Source: Bank for International Settlements. Triennial Central BankSurvey. Report on Global Foreign Exchange Market Activity in 2013.Basel, December, 2013.



Literature






11/ 126

Table 2.3: Geographical distributionof global foreign exchange market turnover,2 daily averages in billions of US dollars and percentages

2004 2010 2013

United Kingdom 835 (32%) 1854 (36,8%) 2726 (40,9%)United States 499 (19,1%) 904 (17,9%) 1263 (18,9%)Singapore 134 (5,1%) 266 (5,3%) 383 (5,7%)Japan 207 (8%) 312 (6,2%) 374 (5,6%)Hong Kong SAR 106 (4,1%) 238 (4,7%) 275 (4,1%)Switzerland 85 (3,3%) 249 (4,9%) 216 (3,2%)

Total 2608 (100%) 5043 (100%) 6671 (100%)

Source: Bank for International Settlements. Triennial Central BankSurvey. Report on Global Foreign Exchange Market Activity in 2013.Basel, December, 2013.



Literature






12/ 126

The interbank market: the largest commercialbanks and securities dealers.Commercial companies.Central banks.Hedge funds.Investment management firms.Retail foreign exchange traders.Non-bank foreign exchange companies.Money transfer/remittance companies andbureaux de change.



Literature






12/ 126




Literature






12/ 126




Literature






12/ 126




Literature






12/ 126




Literature






12/ 126




Literature






12/ 126




Literature






12/ 126




Literature






13/ 126

Market maker

A market maker

or liquidity provider is a company, or an individual, thatquotes both a buy and a sell price in a financial instrument orcommodity held in inventory, hoping to make a profit on thebid-offer spread, or turn.

The U.S. Securities and Exchange Commission definesa "market maker" as a firm that stands ready to buy andsell stock on a regular and continuous basis at a publiclyquoted price.A Designated Primary Market Maker (DPM) is aspecialized market maker approved by an exchange toguarantee that he or she will take the position in aparticular assigned security, option or option index



Literature






13/ 126

Market maker

A market maker

or liquidity provider is a company, or an individual, thatquotes both a buy and a sell price in a financial instrument orcommodity held in inventory, hoping to make a profit on thebid-offer spread, or turn.

The U.S. Securities and Exchange Commission definesa "market maker" as a firm that stands ready to buy andsell stock on a regular and continuous basis at a publiclyquoted price.A Designated Primary Market Maker (DPM) is aspecialized market maker approved by an exchange toguarantee that he or she will take the position in aparticular assigned security, option or option index



Literature






14/ 126

Large market makers

General forex: Barclays Bank Plc (LSE: BARC.L),JPMorgan Chase & Co (JPM), Union Bank ofSwitzerland (UBS), Mizuho Financial Group, Inc.(MHFG), Deutsche Bank AG (DBK)USD/CHF: Union Bank of Switzerland (UBS), CreditSuisse Group (CS.N).Exotic currencies: Standard Chartered Bank(STAN.L). Russian ruble: Alfabank, Sberbank ect.



Literature






15/ 126

Financial markets information

ReutersDow JonesBloomberg



Literature






15/ 126





Literature






15/ 126





Literature






16/ 126

Financial centres

A financial centre

is a location that is home to a cluster of nationally orinternationally significant financial services providers such asbanks, investment managers or stock exchanges.

The International Monetary Fund definition

International Financial Centers (IFCs)—such as London,New York, and Tokyo—are large international full-servicecenters with advanced settlement and payments systems,supporting large domestic economies, with deep and liquidmarkets where both the sources and uses of funds arediverse, and where legal and regulatory frameworks areadequate to safeguard the integrity of principal-agentrelationships and supervisory functions.



Literature






17/ 126

(a) Global Financial CentresIndex (GFCI)

(b) International FinancialCentres Development Index(IFCDI)

Figure 2.1: Financial Centres ranking

GFCI - London-based British think-tank Z/Yen, Qatar Financial Centre Authority;IFCDI - The Xinhua News Agency of China, The Chicago Mercantile Exchange andDow Jones Company of the United States.



Literature






18/ 126

Figure 2.2: New York City’s Financial District in LowerManhattan, which includes Wall Street. Many financial firmshave expanded northward to Midtown Manhattan.



Literature






19/ 126

Figure 2.3: The City of London is one of the oldest financialcentres and today remains at the heart of London’s financialservices industry



Literature






20/ 126

Figure 2.4: Frankfurt’s banking district, home of theEuropean Central Bank.



Literature






21/ 126

Figure 2.5: The Central District of Hong Kong, one of themain financial centres in Asia



Literature






22/ 126

Understanding currency quote

When a currency is quoted, it is done in relation toanother currency, so that the value of one isreflected through the value of another.USD/JPY = 102.50.The base currency is set to the left of the slash,while the currency on the right is referred to as thequote or counter currency



Literature






22/ 126





Literature






22/ 126





Literature






23/ 126

Direct and indirect quote

In a direct currency quote the domestic currency isthe base currency. The direct quote varies theforeign currency, and the quoted, or domesticcurrency, remains fixed at one unit.In an indirect quote the domestic currency is thequoted currency. The domestic currency isvariable and the foreign currency is fixed at oneunit.



Literature






23/ 126

Direct and indirect quote

In a direct currency quote the domestic currency isthe base currency. The direct quote varies theforeign currency, and the quoted, or domesticcurrency, remains fixed at one unit.In an indirect quote the domestic currency is thequoted currency. The domestic currency isvariable and the foreign currency is fixed at oneunit.



Literature






24/ 126

U.S. dollar as a base currency in the currency pair.The Queen’s currencies: the British pound,Australian Dollar and New Zealand dollar - are allquoted as the base currency against the U.S.dollar. The euro is quoted the same way as well.



Literature






24/ 126

U.S. dollar as a base currency in the currency pair.The Queen’s currencies: the British pound,Australian Dollar and New Zealand dollar - are allquoted as the base currency against the U.S.dollar. The euro is quoted the same way as well.



Literature






25/ 126

Example of the currency quotes

Figure 2.6: Currency quotes example

Most currency exchange rates are quoted out to fivedigits after the decimal place, with the exception of theJapanese yen (JPY), which is quoted out to threedecimal places.



Literature






26/ 126

Cross currency pairs

When a currency quote is given without the U.S.dollar as one of its components, this is called across currency. The most common cross currencypairs are the EUR/GBP, EUR/CHF and EUR/JPY.



Literature






27/ 126

Bid and Ask price

When buying a currency pair (going long), the askprice refers to the amount of quoted currency thathas to be paid in order to buy one unit of the basecurrency, or how much the market will sell one unitof the base currency for in relation to the quotedcurrency.When selling a currency pair (going short) the bidprice reflects how much of the quoted currencywill be obtained when selling one unit of the basecurrency, or how much the market will pay for thequoted currency in relation to the base currency.



Literature






27/ 126

Bid and Ask price

When buying a currency pair (going long), the askprice refers to the amount of quoted currency thathas to be paid in order to buy one unit of the basecurrency, or how much the market will sell one unitof the base currency for in relation to the quotedcurrency.When selling a currency pair (going short) the bidprice reflects how much of the quoted currencywill be obtained when selling one unit of the basecurrency, or how much the market will pay for thequoted currency in relation to the base currency.



Literature






28/ 126

Whichever currency is quoted first (the base currency)is always the one in which the transaction is beingconducted. Operator either buys or sells the basecurrency.



Literature






29/ 126

Spread, pips and points

The difference between the bid price and the askprice.EUR/USD = 1.25155/035, the spread would be0.00035 or 35 pips, also known as points.The pip is the smallest amount a price can movein any currency quote. In the case of the U.S.dollar, euro, British pound or Swiss franc, one pipwould be 0.00001. With the Japanese yen, onepip would be 0.001, because this currency isquoted to two decimal places.



Literature






29/ 126





Literature






29/ 126





Literature






30/ 126

Long and short positions

A long position in a security, such as a stock or a bond, orequivalently to be long in a security, means the holder of theposition owns the security and will profit if the price of thesecurity goes up.Short selling (also known as shorting or going short) is thepractice of selling securities or other financial instrumentsthat are not currently owned, and subsequentlyrepurchasing them ("covering").Net position is the difference between total open long(receivable) and open short (payable) positions in a givenasset (security, foreign exchange currency, commodity, etc.)held by an individual. This also refers to the amount ofassets held by a person, firm, or financial institution, as wellas the ownership status of a person’s or institution’sinvestments.



Literature






30/ 126





Literature






30/ 126





Literature






31/ 126

Short positions on the stock exchange

Figure 2.7: Short trade scheme



Literature






32/ 126

Sources of short interest data

Time delayed short interest data (for legally shorted shares)is available in a number of countries, including the US, theUK, Hong Kong, and Spain.The number of stocks being shorted on a global basis hasincreased in recent years for various structural reasonsMarket data providers (Data Explorers, SunGard FinancialSystems) believe that stock lending data provides a goodproxy for short interest levels (excluding any naked shortinterest).SunGard provides daily data on short interest by trackingthe proxy variables based on borrowing and lending datawhich it collects.



Literature






32/ 126





Literature






32/ 126





Literature






32/ 126





Literature






33/ 126

Selling short on the currency markets

Currencies are traded in pairs, each currencybeing priced in terms of another. In this way,selling short on the currency markets is identicalto going long on stocks.A contract is always long in terms of one mediumand short another.When the exchange rate has changed, the traderbuys the first currency again; this time he getsmore of it, and pays back the loan. Since he gotmore money than he had borrowed initially, hemakes money.



Literature






33/ 126





Literature






33/ 126





Literature






34/ 126

Table 2.4: Bank trades during the day

Currency trade RE Currency position

Bought Sold Long Short

100 000 EUR 119 040 USD 1.1904 100 000 EUR 119 040 USD100 000 USD 11 785 000 JPY 117.85 100 000 USD 11 785 000 JPY122 087 USD 70 000 GBP 1.7441 122 087 USD 70 000 GBP

Net position 103 047 USD 11 785 000 JPY100 000 EUR 70 000 GBP

Table 2.5: Next day currency quotes

EURUSD 1,2023 Bank closes down long EURUSDJPY 119.1464 Bank closes down short JPY

GBPUSD 1,7371 Bank closes down short GPB



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) =

1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) =

1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) =

490USD



Literature






35/ 126

Solution

100000EUR · (1.2023 − 1.1904) = 1190USD

− 11785000JPY · (1

119.1464−

1117.85

) = 1087.74USD

− 70000GBP · (1.7371 − 1.7441) = 490USD



Literature






36/ 126

Currency Arbitrage

Currency arbitrage

is the practice of taking advantage of exchange ratesdifference between two or more marketsArbitrage opportunity for USD/CHF: Citibank is quoting0.8745-55. Deutsche Bank is quoting 0.8725-35.

Trader could buy USD10 mln at Deutsche Bank’soffer price of 0.8735 and simultaneously sellUSD10 mln to Citibank at their bid price of 0.8745francs.

This would earn a profit of SF0.0010 per dollartraded, or SF10,000 would be the total arbitrageprofit.



Literature






36/ 126

Currency Arbitrage

Currency arbitrage

is the practice of taking advantage of exchange ratesdifference between two or more marketsArbitrage opportunity for USD/CHF: Citibank is quoting0.8745-55. Deutsche Bank is quoting 0.8725-35.

Trader could buy USD10 mln at Deutsche Bank’soffer price of 0.8735 and simultaneously sellUSD10 mln to Citibank at their bid price of 0.8745francs.This would earn a profit of SF0.0010 per dollartraded, or SF10,000 would be the total arbitrageprofit.



Literature






37/ 126

Triangular arbitrage

USDCHF GBPUSD GBPCHF

New York 0,9987 1,3947

1,3929

London – 1,3947 1,3920Geneva 0,9987 – 1,3920

Table appears to have no possible arbitrage opportunity.

Computing the implicit cross rate for New York, thearbitrageur finds the implicit cross rate to beGBPCHF = 0,9987 · 1,3947 = 1,3929.Thus the cost of GBP is high in New York, and the costof CHF is low.



Literature






37/ 126

Triangular arbitrage

USDCHF GBPUSD GBPCHF

New York 0,9987 1,3947 1,3929London – 1,3947 1,3920Geneva 0,9987 – 1,3920

Table appears to have no possible arbitrage opportunity.

Computing the implicit cross rate for New York, thearbitrageur finds the implicit cross rate to beGBPCHF = 0,9987 · 1,3947 = 1,3929.Thus the cost of GBP is high in New York, and the costof CHF is low.



Literature






38/ 126

Short-term and Long-term ForeignExchange Movements

Causes of short-term (throughout the day) FXmovements:• inventory control;• asymmetric information effects.

In the long run, economic factors affect theexchange rate movements:• demand/ supply of foreign and domestic goods);• Government policy change;• Economic growth and inflation.



Literature






39/ 126

Russian foreign exchange market

Moscow Exchange Group (http://moex.com) is arouble liquidity centre and the oldest regulateddomestic FX trading venue, operating since 1992.The Central Bank of the Russian Federation setsthe official RUB exchange rate based onexchange trading results. FX Market memberspost full or partial collateral to execute their trades.Trades are settled on a payment vs. paymentbasis, whereby delivery is made when a memberfulfils all of its obligations to the the NationalClearing Centre (NCC) which acts as the centralcounterparty and is responsible for centralisedclearing.



Literature






39/ 126





Literature






39/ 126





Literature






40/ 126

Moscow Exchange offers trading in thefollowing currencies

Settlement in Russian rubles (RUB): U.S dollar(USD), euro (EUR), U.S. dollar-euro basket (BKT),Chinese yuan (CNY), Ukrainian hryvnia (UAH),Kazakh tenge (KZT), and Belarusian ruble (BYR).Settlement in U.S. dollars: Euro.

In 2013 spot trades totalled RUB 57 trln and swaptrades amounted to RUB 99 trln.



Literature






40/ 126

Moscow Exchange offers trading in thefollowing currencies

Settlement in Russian rubles (RUB): U.S dollar(USD), euro (EUR), U.S. dollar-euro basket (BKT),Chinese yuan (CNY), Ukrainian hryvnia (UAH),Kazakh tenge (KZT), and Belarusian ruble (BYR).Settlement in U.S. dollars: Euro.

In 2013 spot trades totalled RUB 57 trln and swaptrades amounted to RUB 99 trln.



Literature






41/ 126

Trade-weighted Exchange Rate Indexes

An exchange rate index is a weighted average of acurrency’s value relative to other currencies, withthe weights typically based on the importance ofeach currency to international trade.The Russian Central Bank calculates the valuedual-currency busket as the sum of rouble valuesof 0.55 US dollars and 0.45 euros. The roublevalue of the dual-currency basket has been theoperational indicator of the Bank of Russiaexchange rate policy since February 2005.



Literature






41/ 126

Trade-weighted Exchange Rate Indexes

An exchange rate index is a weighted average of acurrency’s value relative to other currencies, withthe weights typically based on the importance ofeach currency to international trade.The Russian Central Bank calculates the valuedual-currency busket as the sum of rouble valuesof 0.55 US dollars and 0.45 euros. The roublevalue of the dual-currency basket has been theoperational indicator of the Bank of Russiaexchange rate policy since February 2005.



Literature






42/ 126

Figure 2.8: The values of the dual currency basketcalculated by The Central Bank of Russian Federation

Source: The Central Bank of Russian Federation.2016. http://www.cbr.ru/



Literature


International MonetaryArrangementsThe Gold Standardand Interwar PeriodThe Bretton WoodsAgreementFloating ExchangeRatesPlaza and LouvreAccordThe EuropeanMonetary System




43/ 126

Content

2. International Monetary Arrangements2.1 The Gold Standard and Interwar Period2.2 The Bretton Woods Agreement2.3 Floating Exchange Rates2.4 Plaza and Louvre Accord2.5 The European Monetary System



Literature






43/ 126

The Gold Standard: 1880 to 1914. TheInterwar Period: 1918 to 1939

Under a gold standard, currencies are valued interms of their gold equivalent (an ounce of goldwas worth USD20.67 in terms of the U.S. dollarover the gold standard period).The I World War ended Britain’s financialpreeminence.The United States had risen to the status of theworld’s dominant banker country.



Literature






43/ 126





Literature






43/ 126





Literature






44/ 126

Table 3.1: Leading central bank/treasury gold reserves(inmetric tons fine gold)

Year 1845 1850 1855 1860 1865 1870 1875 1880

UK 82 104 74 78 93 161 154 170France 2 3,5 32,8 105 194 217 337 242Germany n/a n/a n/a n/a n/a n/a 43 81Italy n/a n/a n/a n/a n/a 30,8 26 22Russia n/a n/a 81 n/a 57 160 230 195USA n/a n/a n/a n/a n/a 107 87 208

Source: World Gold Council. Historical Data - Annual time serieson World Official Gold Reserves since 1845. 10th August 2011.



Literature






45/ 126


Year 1885 1890 1895 1900 1905 1910 1913 1915

UK 141 166 305 198 199 223 248 585France 344 370 460 544 836 952 1030 1457Germany 99 186 252 211 267 240 437 876Italy 142 133 132 115 285 350 355 397Russia 195 312 695 661 654 954 1233 1250USA 371 442 169 602 1149 1660 2293 2568




Literature






46/ 126


Year 1920 1925 1930 1935 1940 1945

UK 864 1045 1080 1464 n/a 1773France 1622 1201 3160 3907 1773 1378Germany 391 432 794 56 n/a n/aItaly 307 498 420 240 122 28Russia n/a 141 375 7456 n/a n/aUSA 3679 5998 6358 8998 19543 17848




Literature






47/ 126

So a run on U.S. gold at the end of 1931 led to a15 percent drop in U.S. gold holdings. By 1933 theUnited States abandoned the gold standard.The early to mid-1930s was a period ofcompetitive devaluations and foreign exchangecontrols.



Literature






47/ 126

So a run on U.S. gold at the end of 1931 led to a15 percent drop in U.S. gold holdings. By 1933 theUnited States abandoned the gold standard.The early to mid-1930s was a period ofcompetitive devaluations and foreign exchangecontrols.



Literature






48/ 126

The Bretton Woods Agreement: 1944 to1973 and its breakdown

Bretton Woods agreement required each countryto fix the value of its currency in terms of ananchor currency, namely the dollar.The U.S. dollar was the key currency in thesystem, and USD1 was defined as being equal invalue to 1/35 ounce of gold.Since every currency had an implicitly defined goldvalue, through the link to the dollar, all currencieswere linked in a system of fixed exchange rates.



Literature






48/ 126





Literature






48/ 126





Literature






49/ 126

Nations were committed to maintaining the parityvalue of their currencies within 1 percent of parity.When a country was experiencing difficultymaintaining its parity value because of balance ofpayments disequilibrium, it could turn to theInternational Monetary Fund (IMF).



Literature






49/ 126

Nations were committed to maintaining the parityvalue of their currencies within 1 percent of parity.When a country was experiencing difficultymaintaining its parity value because of balance ofpayments disequilibrium, it could turn to theInternational Monetary Fund (IMF).



Literature






50/ 126

The IMF was created to monitor the operation ofthe system and provide short-term loans tocountries experiencing temporary balance ofpayments difficulties.IMF conditions for loans were changes indomestic economic policy aimed at restoringbalance of payments equilibrium.



Literature






50/ 126

The IMF was created to monitor the operation ofthe system and provide short-term loans tocountries experiencing temporary balance ofpayments difficulties.IMF conditions for loans were changes indomestic economic policy aimed at restoringbalance of payments equilibrium.



Literature






51/ 126

The failure to realign currency values in the face offundamental economic change spelled thebeginning of the end for the gold exchangestandard of the Bretton Woods agreement by thelate 1960s.In December 1971, the dollar per gold exchangevalue was changed from USD35 to USD38.02 perounce of gold. But the dollar was still inconvertibleinto gold.The speculative capital flows of 1972 and early1973 led to a further devaluation of the dollar inFebruary 1973, when the official price of an ounceof gold rose from USD38 to USD42.22.In March 1973, the major currencies began to float



Literature






51/ 126




Literature






51/ 126




Literature






51/ 126




Literature






52/ 126

Floating Exchange Rates: starting from1973

The types of exchange rate systems1. Free floating.2. Managed floating.3. Horizontal bands.4. Crawling pegs.5. Crawling bands.6. Fixed peg.7. Currency board.8. “Dollarization” or No separate legal tender.



Literature






53/ 126

“dollarization” where the central bank of thecountry has completely given up control of themoney supply to adopt some other country’scurrencypurely floating, where the central bank retainsdomestic control over the currency in the country.In between, the central bank has some degree ofcontrol over the money supply.



Literature






53/ 126




Literature






53/ 126




Literature






54/ 126

What is “Legal Tender”

Legal tender

is any official medium of payment recognized by lawthat can be used to extinguish a public or private debt,or meet a financial obligation. The national currency islegal tender in practically every country. A creditor isobligated to accept legal tender toward repayment of adebt. Legal tender can only be issued by the nationalbody that is authorized to do so, such as the U.S.Treasury in the United States and the Royal CanadianMint in Canada.The term "legal tender" is from Middle English tendren,French tendre (verb form), meaning to offer. The Latinroot is tendere (to stretch out), and the sense of tenderas an offer is related to the etymology of the Englishword "extend" (to hold outward).



Literature






55/ 126

What does “Tender” mean

To tender

To invite bids for a project, or to accept a formal offersuch as a takeover bid. Tender usually refers to theprocess whereby governments and financialinstitutions invite bids for large projects that must besubmitted within a finite deadline. The term also refersto the process whereby shareholders submit theirshares or securities to a takeover offer.



Literature






56/ 126

Legal Tender and Standard of DeferredPayment

A debt is a deferred payment; a standard of deferredpayment is what they are denominated in.Since the value of money – be it dollars, gold, or others– may fluctuate over time via inflation and deflation, thevalue of deferred payments (the real level of debt)likewise fluctuates.A device is termed “legal tender” if it may serve todischarge (pay off) debts; thus, while US dollars arenot backed by gold or any other commodity, they drawvalue from being legal tender – being usable to pay offdebts.



Literature






57/ 126

Characteristics Associated with CountriesChoosing to Peg or Float

Peggers Floaters

Small size Large sizeOpen economy Closed economy

Harmonious inflation rate Divergent inflation rateConcentrated trade Diversified trade



Literature






58/ 126

Plaza Accord

Between 1980 and 1985 the dollar hadappreciated by about 50% against the Japaneseyen, Deutsche Mark, French Franc and BritishpoundCampaign asking for protection against foreigncompetitionThe governments of France, West Germany,Japan, the United States, and the United Kingdomsigned the accord to depreciate the U.S. dollar inrelation to the Japanese yen and GermanDeutsche Mark by intervening in currency marketson September 22, 1985 at the Plaza Hotel in NewYork City.The exchange rate value of the dollar versus theyen declined by 51% from 1985 to 1987.



Literature






58/ 126

Plaza Accord




Literature






58/ 126

Plaza Accord




Literature






58/ 126

Plaza Accord




Literature






59/ 126

Louvre Accord

The Louvre Accord was an agreement, signed onFebruary 22, 1987 in Paris, that aimed to stabilizethe international currency markets and halt thecontinued decline of the US Dollar caused by thePlaza Accord.The Louvre Accord helped prevent a recessionbecause it stopped the value of the U.S. Dollarfrom decreasing any further in relation to othercurrencies.Countries agreed to reduce budget deficits andgovernment spendings, cut taxes, USA agreed tohold interest rates low.



Literature






59/ 126

Louvre Accord




Literature






59/ 126

Louvre Accord




Literature






60/ 126

The European Monetary System and theEuro

The European Monetary System (EMS) wasestablished in March 1979.The member countries agreed to maintain smallexchange rate fluctuations among themselves,while allowing free float against outsidecurrencies.



Literature






60/ 126

The European Monetary System and theEuro

The European Monetary System (EMS) wasestablished in March 1979.The member countries agreed to maintain smallexchange rate fluctuations among themselves,while allowing free float against outsidecurrencies.



Literature






61/ 126

The theory of optimum currency areaProfessor Robert Mundell of Columbia University, 1961

Criterion for a common currency zone

The relevant criterion for identifying and designing acommon currency zone is the degree of factor (i.e.,capital and labor) mobility within the zone; a highdegree of factor mobility would provide an adjustmentmechanism, providing an alternative tocountry-specific monetary/currency adjustments.



Literature






62/ 126

Monetary Unions I

Monetary union Participants

European Union(EU)

Austria, Belgium, Bulgaria, Cyprus,Czech Republic, Germany, Den-mark, Spain, Estonia, Finland,France, United Kingdom, Greece,Croatia, Hungary, Ireland, Italy,Lithuania, Luxembourg, Latvia,Malta, Netherlands, Poland, Portu-gal, Romania, Slovakia, Slovenia,Sweden

CommonwealthofIndependentStates (CIS)

Armenia, Azerbaijan, Belarus,Kazakhstan, Kyrgyzstan, Moldova,Russia, Tajikistan, Uzbekistan

Asian MonetaryUnit (AMU)

Australia, Brunei, China, Indone-sia, India, Japan, Cambodia, SouthKorea, Laos, Myanmar, Malaysia,New Zealand, Philippines, Singa-pore, Thailand, Vietnam



Literature






63/ 126

Monetary Unions II

Monetary union Participants

East African Commu-nity (EAC)

Burundi, Kenya, Rwanda,Tanzania, Uganda

Economic CommunityofWest African States(Ecowas)

Benin, Burkina Faso,CapeVerde, Gambia, Ghana,Guinea, Guinea-Bissau, IvoryCoast, Liberia, Mali, Niger,Nigeria, Senegal, SierraLeone, Togo

Bolivarian Alliance forthe Peoples of OurAmerica (AlBA)

Antigua and Barbuda, Bo-livia, Cuba, Dominica,Ecuador, Grenada, SaintKitts and Nevis, Saint Lucia,Nicaragua, Saint Vincent andthe Grenadines, Venezuela



Literature






64/ 126

Existing and emerging monetary unions



Literature






65/ 126

Convergence of monetary policy

the country’s inflation rate did not exceed theaverage of the lowest three member country ratesby more than 1.5 percentage points;its interest rate on long-term government bondsdid not exceed those of the three lowest-inflationmembers by more than 2 percentage points;the country’s government budget deficit did notexceed 3 percent of GDP, and outstandinggovernment debt did not exceed 60 percent ofGDP.



Literature






65/ 126





Literature






65/ 126





Literature






66/ 126

The optimum currency area

The geographical region that could gain economicefficiency by fixing exchange rates within a groupand floating exchange rates with the rest of theworld.Necessary condition is perfect mobility of thefactors of production.



Literature






66/ 126

The optimum currency area

The geographical region that could gain economicefficiency by fixing exchange rates within a groupand floating exchange rates with the rest of theworld.Necessary condition is perfect mobility of thefactors of production.



Literature






67/ 126

The European Central Bank (ECB)

Created on June 1, 1998, in Frankfurt, Germany.The European Central Bank (ECB) is responsiblefor monetary policy of the Eurozone.The ECB is governed by a president and a boardof the heads of national central banks.The main purpose of the ECB is to keep inflationunder control.



Literature






67/ 126





Literature






67/ 126





Literature






67/ 126





Literature






68/ 126

The new European currency, the euro, made itsdebut on January 1, 1999. The symbol is , and theISO code is EUR.In the transition years of 1999 to 2001, peopleused the euro as a unit of account, denominatingfinancial asset values and transactions in euroamounts. Bank accounts were available in eurosand credit transactions were denominated ineuros.Euro notes and coins began to circulate onJanuary 1, 2002.



Literature






68/ 126




Literature






68/ 126




Literature






69/ 126

Member states

As of August 2014, the Euro was adopted by 18member states of European Union:Austria (1999), Belgium (1999), Cyprus (2008),Estonia (2011), Finland (1999), France (1999),Germany (1999), Greece (2001), Ireland (1999), Italy(1999), Latvia (2014), Luxembourg (1999), Malta(2008), the Netherlands (1999), Portugal (1999),Slovakia 2009), Slovenia (2007), and Spain (1999).



Literature



The Balance ofPayments (BoP)The BoP componentsThe BoP transactionsclassificationBoP Equilibrium andAdjustmentThe Russian ForeignDebt



70/ 126

Content

3. The Balance of Payments (BoP)3.1 The BoP components3.2 The BoP transactions classification3.3 BoP Equilibrium and Adjustment3.4 The Russian Foreign Debt



Literature






70/ 126

Balance of payments accounts are an accountingrecord of all monetary transactions between acountry and the rest of the world.Balance of payments data are reported quarterlyfor most developed countries.If any particular account has the value of the creditentries that exceeds the debits, the account has asurplus. If the debits exceed the credits, a deficitexists.A surplus or deficit can apply only to a particularaccount of the balance of payments.The balance of payments is always zero.



Literature






70/ 126




Literature






70/ 126




Literature






70/ 126




Literature






70/ 126




Literature






71/ 126

Balance of payments in the IMF‘sterminology

The current account includes the value of trade inmerchandise, services, investment income, andcash transfers.The capital account represents transfers.Transfers are one-way flows, such as gifts, asopposed to commercial exchanges (i.e.,buying/selling and barter).The financial account is the net change inownership of foreign assets. It includes loans,direct and portfolio investments between thecountry and the rest of world, reserve account.



Literature






71/ 126





Literature






71/ 126





Literature






72/ 126

Every country’s major export



Literature






73/ 126

Current account of Russian Federationin millions of US dollars for period from 2005 to 1Q 2014

Indicator 2005 2008 2011 2013 Q1 2014

Currentaccount

84389 103935 97274 34141 27089

Goods andservices

104560 157206 163398 123661 40022

Goods 116185 177625 196854 181939 50728Services -11626 -20420 -33456 -58277 -10707Primary income -18526 -46483 -60399 -80246 -10998Compensation ofemployees

-1133 -14357 -9522 -13170 -2361

Investmentincome

-17394 -32125 -51031 -67157 -8664

Secondaryincome

-1645 -6788 -5725 -9274 -1935

Source: Central Bank of Russian Federation, www.cbr.ru. 2014.



Literature






74/ 126

Current account of Russian Federationin millions of US dollars for period from 2005 to 1Q 2014



Literature






75/ 126

Capital account of Russian Federationin millions of US dollars for period from 2005 to 1Q 2014

Indicator 2005 2008 2011 2013 Q1 2014

Capital account -12387 -104 130 -395 -185

acquisitions (debit)/disposals (credit) ofnonproducednonfinancial assets

-57 -309 38 -146 -191

Capital transfers -12331 205 92 -249 6General government -12331 205 4 -430 -47Financial corporations,nonfinancialcorporations,households

0 0 88 181 53




Literature






76/ 126

Financial account of Russian Federationin millions of US dollars for period from 2005 to 1Q 2014

Indicator 2005 2008 2011 2013 Q1 2014

Financialaccount

66997 100781 88748 22906 21229

Direct investment 2372 -19120 11767 16058 5627Portfolioinvestment

11443 35691 15277 11011 17635

Financialderivatives

233 1370 1394 346 623

Other investment -8511 121765 47679 17567 24695Reserve assets 61461 -38925 12630 -22077 -27351

Net errors andomissions

-5004 -3051 -8655 -10840 -5675




Literature






77/ 126

Balance of payments of Russian Federationin millions of US dollars for period from 2005 to 1Q 2014

Indicator -2005- -2008- -2011- -2013- Q1 2014

Current account 84389 103935 97274 34141 27089Capital account -12387 -104 130 -395 -185Financialaccount*

-66997 -100781 -88748 -22906 -21229

Net errors andomissions

-5004 -3051 -8655 -10840 -5675

Total** 1 -1 1 0 0

Source: Central Bank of Russian Federation, www.cbr.ru. 2014.* Financial account is reported in previous tables with opposite sign. In factit must be subtracted from the current account.** Total sum not always equals to zero because of rounding errors.



Literature






78/ 126

The balance of payments identity

Expressed with the IMF definition, the balance ofpayments identity can be written:Current account + Capital account + Financial account+ Balancing Item = 0



Literature






79/ 126

The balance of payments transactionsclassification

The balance of payments is composed as abalance sheet using double-entry bookkeeping –every item involves two entries, a credit and adebit.The credits record items lead to payments inflows.Such items are associated with a greater demandfor domestic currency or supply of foreigncurrency to the foreign exchange market.The debits record items lead to paymentsoutflows. These are associated with a greatersupply of domestic currency or demand for foreigncurrency in the foreign exchange market.



Literature






79/ 126





Literature






79/ 126





Literature






80/ 126

Balance of Payments example operationsthousands USD

Current account Credit (+) Debit (−)

Goods 5000(2) Services 25(4)Investment income 25(3)Goods 50(5)

Net

5050

NetCapital account Credit (+) Debit (−)

Corporations&households 5000(1) Corporations&households 5000(1)Corporations&households 25(4) Corporations&households 5000(2)

Corporations&households 25(3)Capital transfers 50(5)Corporations&households 50000(6)

Net Net

55050

Financial account Credit (+) Debit (−)

Reserve assets 50000(6)

Net

50000

NetBalance of payments Credit (+) Debit (−)

Current account 5050 Capital account 55050Financial account 50000

Net

0

Net



Literature






80/ 126


Current account Credit (+) Debit (−)

Goods 5000(2) Services 25(4)Investment income 25(3)Goods 50(5)

Net

5050

NetCapital account Credit (+) Debit (−)Corporations&households 5000(1) Corporations&households 5000(1)

Corporations&households 25(4) Corporations&households 5000(2)Corporations&households 25(3)Capital transfers 50(5)Corporations&households 50000(6)

Net Net

55050



Net

50000



Net

0

Net



Literature






80/ 126


Current account Credit (+) Debit (−)Goods 5000(2)

Services 25(4)Investment income 25(3)Goods 50(5)

Net

5050


Corporations&households 25(4)



Net Net

55050



Net

50000



Net

0

Net



Literature






80/ 126


Current account Credit (+) Debit (−)Goods 5000(2)

Services 25(4)

Investment income 25(3)

Goods 50(5)

Net

5050



Corporations&households 5000(2)Corporations&households 25(3)

Capital transfers 50(5)Corporations&households 50000(6)

Net Net

55050



Net

50000



Net

0

Net



Literature






80/ 126


Current account Credit (+) Debit (−)Goods 5000(2) Services 25(4)Investment income 25(3)

Goods 50(5)

Net

5050

NetCapital account Credit (+) Debit (−)Corporations&households 5000(1) Corporations&households 5000(1)Corporations&households 25(4) Corporations&households 5000(2)


Capital transfers 50(5)Corporations&households 50000(6)

Net Net

55050



Net

50000



Net

0

Net



Literature






80/ 126


Current account Credit (+) Debit (−)Goods 5000(2) Services 25(4)Investment income 25(3)Goods 50(5)

Net

5050


Corporations&households 25(3)Capital transfers 50(5)


Net Net

55050



Net

50000



Net

0

Net



Literature






80/ 126



Net

5050



Net Net

55050

Financial account Credit (+) Debit (−)Reserve assets 50000(6)

Net

50000



Net

0

Net



Literature






80/ 126



Net 5050 NetCapital account Credit (+) Debit (−)Corporations&households 5000(1) Corporations&households 5000(1)Corporations&households 25(4) Corporations&households 5000(2)


Net Net

55050

Financial account Credit (+) Debit (−)Reserve assets 50000(6)

Net

50000



Net

0

Net



Literature






80/ 126





Net Net 55050Financial account Credit (+) Debit (−)Reserve assets 50000(6)

Net

50000



Net

0

Net



Literature






80/ 126






Net 50000 NetBalance of payments Credit (+) Debit (−)


Net

0

Net



Literature






80/ 126






Net 50000 NetBalance of payments Credit (+) Debit (−)Current account 5050 Capital account 55050Financial account 50000Net

0

Net



Literature






80/ 126






Net 50000 NetBalance of payments Credit (+) Debit (−)Current account 5050 Capital account 55050Financial account 50000Net 0 Net



Literature






81/ 126

Balance of Payments Equilibrium andAdjustment

Balance of payments equilibrium exists whenexports equal imports or credits equal debits onsome particular subaccount.In the case of flexible exchange rates balance ofpayments equilibrium is restored by the operationof the free market.When the exchange rate is fixed the nationalcurrency can be overvalued or undervalued andthe central banks must now finance the tradeimbalance by international reserve flows.Central banks use direct controls on internationaltrade sometimes.



Literature






81/ 126





Literature






81/ 126





Literature






81/ 126





Literature






82/ 126

China is growing its importance

Sources: Khanna, P. (2016). Connectography:mapping the future of global civilization. RandomHouse.



Literature






83/ 126

External Debt of the Russian Federation asof December 2015 (estimate)(millions of US dollars)

Dec. 2013 Dec. 2014 Dec. 2015

Total 728864 599041 515254

1. General Government 61743 41606 307431.1. Federal Government 60962 41027 301801.1.1. New Russian Debt 58949 39257 289391.1.2. Debt of the former USSR 2012 1770 12411.2. Local Government 781 580 5632. Central bank 15963 10599 115283. Banks 214394 171450 1323494. Other sectors 436764 375386 3406334.1. Debt liabilities to direct investorsand to direct investment enterprises

151288 133451 130303

4.2. Loans and deposits 268402 225978 1975594.3. Debt securities 9155 6145 47364.4. Trade credits 3115 3469 28124.5. Financial leases 2105 2433 25014.6. Other 2700 3909 2722




Literature




Forward-looking MarketInstrumentsThe currency forwardsThe foreign exchangeswapsThe currency swapsThe foreign exchangefuturesThe foreign exchangeoptionsPricing forex options


84/ 126

Content

4. Forward-looking Market Instruments4.1 The currency forwards4.2 The foreign exchange swaps4.3 The currency swaps4.4 The foreign exchange futures4.5 The foreign exchange options4.6 Pricing forex options



Literature






84/ 126

The currency forwards

The currency forward

is a contract in the foreign exchange market that locksin the exchange rate for the purchase or sale of acurrency on a future date.

A currency forward represents a bindingobligation, which means that the contract buyer orseller cannot walk away if the “locked in” rateeventually proves to be adverse.To compensate for the risk of non-delivery,financial institutions may require a deposit fromretail investors or smaller firms with whom they donot have a business relationship.



Literature






84/ 126

The currency forwards

The currency forward

is a contract in the foreign exchange market that locksin the exchange rate for the purchase or sale of acurrency on a future date.

A currency forward represents a bindingobligation, which means that the contract buyer orseller cannot walk away if the “locked in” rateeventually proves to be adverse.To compensate for the risk of non-delivery,financial institutions may require a deposit fromretail investors or smaller firms with whom they donot have a business relationship.



Literature






85/ 126

Determining a currency forward rate

F =Bid + Ask

2·

1 + i1 · n365

1 + i2 · n365

(5.1)

whereF – forward rate;Bid, Ask – spot bid and ask rate respectively;i1 – annual interest rate for quoted currency;i2 – annual interest rate for base currency;n – forward contract period in days



Literature






86/ 126

Forward rate calculation

assume a current spot rate for the Russian ruble ofUS$1 = RUR76.45 or USD/RUR=76.45, a one-yearinterest rate for Russian rubles of 8% (key rate held bythe Central Bank of Russian Federation), and one-yearinterest rate for US dollars of 0.25%. Assume thatUSD/RUR bid and ask are 75.00 and 76.0 respectively.So, 3-months (3M) forward interest rate would be

F3M;USDRUB =

75 + 762

·1 + 0.08 · 90

365

1 + 0.0025 · 90365

F3M;USDRUB = 76,9419



Literature






86/ 126



F3M;USDRUB =75 + 76

2·

1 + 0.08 · 90365

1 + 0.0025 · 90365




Literature






86/ 126



F3M;USDRUB =75 + 76

2·

1 + 0.08 · 90365

1 + 0.0025 · 90365




Literature






87/ 126

A foreign exchange swap

is an arrangement where there is a simultaneousexchange of two currencies on a specific date at a rateagreed at the time of the contract, and a reverseexchange of the same two currencies at a date furtherin the future at a rate agreed at the time of the contract.

A foreign exchange swap consists of two legs:1) a spot foreign exchange transaction, and;2) a forward foreign exchange transaction.



Literature






88/ 126

The forward points or swap points

are quoted as the difference between forward andspot: F − S.

F − S = S(1 + i1 · n

base

1 + i2 · nbase

− 1)

=S(i1 − i2)T

1 + i2T≈ S(i1 − i2)T (5.2)

where n - forward contract term;T = n

base ;base = 365 or 366. If i2T is small. Thus, the value ofthe swap points is roughly proportional to the interestrate differential.The most common use of foreign exchange swaps isfor institutions to fund their foreign exchange balances



Literature






89/ 126

Swap points calculation

Table 5.1: Assume that we have suchRUB and USD interest rates

%RUB 8%

%USD 0,25%n 90base 365SWUSDRUB

0,01911



Literature






89/ 126

Swap points calculation

Table 5.1: Assume that we have suchRUB and USD interest rates

%RUB 8%

%USD 0,25%n 90base 365SWUSDRUB 0,01911



Literature






90/ 126

A currency swap is a contract in which twocounterparties exchange streams of interestpayments in different currencies for an agreedperiod of time and then exchange principalamounts in the respective currencies at an agreedexchange rate at maturity.Currency swaps allow firms to obtain long-termforeign currency financing at lower cost than theycan by borrowing directly



Literature






90/ 126

A currency swap is a contract in which twocounterparties exchange streams of interestpayments in different currencies for an agreedperiod of time and then exchange principalamounts in the respective currencies at an agreedexchange rate at maturity.Currency swaps allow firms to obtain long-termforeign currency financing at lower cost than theycan by borrowing directly



Literature






91/ 126

Table 5.2: Loan rates for two firms in different currencies

USD interest rate, % EUR interest rate, %

Firm A 10 7Firm B 9 8

Suppose, US firm has free access to loans from USbanks, but can not have such favorable opportunitieson Germany capital market.Similarly, the German firm can have good loanconditions in the homeland, but far less favorable onesin the USA.By currency swap agreement both firms can usecomparative advantages of each other to reduce thecost of loan.



Literature






92/ 126

Cash flows of the two borrowersin currency swap agreement

Company A

German Bank

Company B

USA Bank

(1)10mlnEUR

(6)0.7mlnEUR

(10)10mlnEUR

(8)12.5mlnUSD

(7)1.125mlnUSD

(3)12.5mlnUSD

(2)10mlnEUR →(9)← 12.5mlnUSD(4)1.25mlnUSD →(5)← 0.8mlnEUR

Figure 5.1: Currency swap



Literature






93/ 126

Thus, both firms obtain the loans in necessary foreigncurrency at a lower rate, than it would be in case of therequest for the credit directly in foreign bank. As awhole the Firm A saves on interest payments 0,8 ml –0,7 ml = 0,1 ml EUR, and the Firm B saves on interestpayments 1,25 ml – 1,125 ml = 0,125 ml USD.



Literature






94/ 126

Futures are similar to forward contracts. Each futurecontract has a fixed amount and pre-determined dates.The difference of futures from forwards consists in thefollowing:1. Futures trading is carried out on the open exchangemarket, and forwards – on interbank. Therefore datesof future contracts expiration are attached to certaindates. Futures contracts are standardized onexpiration periods, volumes and terms of delivery. Incase of forward contracts expiration periods andvolumes of the transaction are determined by themutual arrangement of the parties.2. Futures are traded only on most liquid currencypairs. Forward contracts are traded almost on allcurrency pairs.



Literature






95/ 126

3. The futures market is available not only to biginvestors, but also small. The forward market is limitedby that the minimum sum for the transaction amounts500 thousand US dollars.4. For about 95% futures trading volume come to anend with the conclusion of the opposite transaction,thus there is no real delivery of the currency. Theparties receive only a difference between the initialprice of the contract and the price existing in the day ofthe closing transaction. On the contrary, for about 95%forwards transactions come to an end with currencydelivery.5. Futures transactions cost are cheaper because ofstandardization.



Literature






96/ 126

Foreign currency options

are contracts that give a buyer the right to buy (calloption) or sell (put option) currencies at a specifiedprice within a specific period of time. The strike price isthe price at which the owner of the contract has theright but not the obligation to transact.



Literature






97/ 126

Comparison of currency call and putoptions I

Currency call option1. In case the currency calloption is executed,expenses of the currencybuyer will make:

Roe = Ro + P,

where Ro – an exchangerate at which the currencywill be acquired;P – premium for the option(buyer‘s expenses).

Currency put option1. In case the currency putoption is executed, revenueof the currency seller willmake:

Roe = Ro − P,

where Ro – an exchangerate at which the currencywill be acquired;P – premium for the option(seller‘s expensesanyway).



Literature






98/ 126

Comparison of currency call and putoptions II

Currency call option2. In case the currency calloption isn’t executed,expenses of the currencybuyer will make:

Rte = Rt + P,

where Rt – the currentmarket currency rate ofexchange.

Currency put option2. In case the currency putoption isn’t executed,revenue of the currencyseller will make:

Rte = Rt − P,

where Rt – the currentmarket currency rate ofexchange.



Literature






99/ 126

Comparison of currency call and putoptions III

Currency call option3. As the buyer isinterested in minimizationof the expenses, acondition under whichexecution of this option willbe favorable to him, will be:

Roe < Rte

orRo < Rt .

Currency put option3. As the seller isinterested in maximizationof the revenue, a conditionunder which execution ofthis option will be favorableto him, will be:

Roe > Rte

orRo > Rt .



Literature






100/ 126

Comparison of currency call and putoptions IV

Currency call option4. The buyer of the calloption will make profit, ifrate of exchange will riseso that it can cover optionpremium, i.e.

Roe + P < Rte

If both sides of inequalityare equal, the trade will bebreak-even.

Currency put option4. The buyer of the putoption will make profit, ifrate of exchange will fall sothat it can cover optionpremium, i.e.

Roe − P > Rte

If both sides of inequalityare equal, the trade will bebreak-even.



Literature






101/ 126

Example

Consider the firm in Russia that needs $1 million US dollarsin 3 months. The firm decided to buy 3-months call optioncontract for USD/RUR

Table 5.3: Currency market conditions

Bid Ask

USD/RUR spot rate 32.5 33.2USD/RUR 3-months forward premium 0.6 0.8USD/RUR 3-month option premium 0.2 0.2

Should the firm execute the option if the Bid/Ask rate ofexchange for USD/RUR makes, respectively, 32.80 and33.40 in three months?



Literature






102/ 126

Solution

If the firm execute the call option, its costs of dollar‘spurchase will make

33,20 + 0,80 + 0,20 = 34,20.If the firm doesn’t execute the option, its expenses willmake:33,40 + 0,20 = 33,60.Thus, option execution will be unprofitable to firm sinceincreases its costs of dollar‘s purchase per 0,60 rublesfor one dollar.



Literature






102/ 126

Solution

If the firm execute the call option, its costs of dollar‘spurchase will make33,20 + 0,80 + 0,20 = 34,20.

If the firm doesn’t execute the option, its expenses willmake:33,40 + 0,20 = 33,60.Thus, option execution will be unprofitable to firm sinceincreases its costs of dollar‘s purchase per 0,60 rublesfor one dollar.



Literature






102/ 126

Solution

If the firm execute the call option, its costs of dollar‘spurchase will make33,20 + 0,80 + 0,20 = 34,20.If the firm doesn’t execute the option, its expenses willmake:

33,40 + 0,20 = 33,60.Thus, option execution will be unprofitable to firm sinceincreases its costs of dollar‘s purchase per 0,60 rublesfor one dollar.



Literature






102/ 126

Solution

If the firm execute the call option, its costs of dollar‘spurchase will make33,20 + 0,80 + 0,20 = 34,20.If the firm doesn’t execute the option, its expenses willmake:33,40 + 0,20 = 33,60.

Thus, option execution will be unprofitable to firm sinceincreases its costs of dollar‘s purchase per 0,60 rublesfor one dollar.



Literature






102/ 126

Solution

If the firm execute the call option, its costs of dollar‘spurchase will make33,20 + 0,80 + 0,20 = 34,20.If the firm doesn’t execute the option, its expenses willmake:33,40 + 0,20 = 33,60.Thus, option execution will be unprofitable to firm sinceincreases its costs of dollar‘s purchase per 0,60 rublesfor one dollar.



Literature





Binomial OptionsPricing Model (BOPM)Market VolatilityBinomial price treeIntermediate OptionValueCall and Put OptionsBinary optionsGeneral one periodmodel

Content

5. Binomial Options Pricing Model (BOPM)5.1 Market Volatility5.2 Binomial price tree5.3 Intermediate Option Value5.4 Call and Put Options5.5 Binary options5.6 General one period model



Literature






Binomial Options Pricing Model (BOPM)

Buyer and seller always have different opinions onthe underlying instrument price directionAt each step, it is assumed that the underlyinginstrument will move up or down by a specificfactor (u or d) per step of the tree (where, bydefinition, u ≥ 1 and 0 < d ≤ 1).The up and down factors are calculated using theunderlying volatility, σ, and the time duration of astep, t , measured in time intervals (days, months,years).Binomial Options Pricing Model says nothingabout the underlying instrument up or down pricemovements probability.



Literature










Literature










Literature










Literature






At each final node of the tree — i.e. at expirationof the option — the option value is simply itsintrinsic, or exercise, value.Max[(Sn − K),0], for a call optionMax[(K˘Sn),0], for a put option:Where K is the strike price and Sn is the spotprice of the underlying asset at the nth period.The binomial pricing model traces the evolution ofthe option‘s key underlying variables indiscrete-time. This is done by means of a binomiallattice (tree), for a number of time steps betweenthe valuation and expiration dates. Each node inthe lattice represents a possible price of theunderlying at a given point in time.



Literature






At each final node of the tree — i.e. at expirationof the option — the option value is simply itsintrinsic, or exercise, value.Max[(Sn − K),0], for a call optionMax[(K˘Sn),0], for a put option:Where K is the strike price and Sn is the spotprice of the underlying asset at the nth period.The binomial pricing model traces the evolution ofthe option‘s key underlying variables indiscrete-time. This is done by means of a binomiallattice (tree), for a number of time steps betweenthe valuation and expiration dates. Each node inthe lattice represents a possible price of theunderlying at a given point in time.



Literature






USDRUB quotes changes from 01.10.2013to 01.10.2014

Date Close price ∆,%

01.10.2013 32,097301.11.2013 33,0852

3,08%

01.12.2013 32,8311

-0,77%

01.01.2014 35,2523

7,37%

01.02.2014 35,9238

1,90%

01.03.2014 35,1707

-2,10%

01.04.2014 35,6287

1,30%

01.05.2014 34,8855

-2,09%

01.06.2014 33,9675

-2,63%

01.07.2014 35,705

5,12%

01.08.2014 37,1041

3,92%

01.09.2014 39,5562

6,61%

01.10.2014 42,9913

8,68%



Literature






USDRUB quotes changes from 01.10.2013to 01.10.2014

Date Close price ∆,%

01.10.2013 32,097301.11.2013 33,0852 3,08%01.12.2013 32,8311 -0,77%01.01.2014 35,2523 7,37%01.02.2014 35,9238 1,90%01.03.2014 35,1707 -2,10%01.04.2014 35,6287 1,30%01.05.2014 34,8855 -2,09%01.06.2014 33,9675 -2,63%01.07.2014 35,705 5,12%01.08.2014 37,1041 3,92%01.09.2014 39,5562 6,61%01.10.2014 42,9913 8,68%



Literature






Monthly USDRUB quotes graph



Literature






Monthly USDRUB quote percentagechange



Literature






USDRUB quotes percentage changeintervals



Literature






Formulas for the average return and thestandard deviation of return

The average return:

m =

∑ni=1 xi

n

where xi – observed value;n – number of values.The standard deviation of return:

s =

√∑ni=1(m − xi)2

n − 1



Literature






Formulas for the average return and thestandard deviation of return

The average return:

m =

∑ni=1 xi

n

where xi – observed value;n – number of values.The standard deviation of return:

s =

√∑ni=1(m − xi)2

n − 1



Literature






Monthly USDRUB average return and itsstandard deviation

xi m − xi (m − xi)2

1 3,08%

-0,54% 0,30

2 -0,77%

3,30% 10,90

3 7,37%

-4,84% 23,44

4 1,90%

0,63% 0,40

5 -2,10%

4,63% 21,44

6 1,30%

1,23% 1,52

7 -2,09%

4,62% 21,34

8 -2,63%

5,17% 26,68

9 5,12%

-2,58% 6,66

10 3,92%

-1,38% 1,92

11 6,61%

-4,08% 16,61

12 8,68%

-6,15% 37,83

Σ

30,40%

-

169,02

m

2,5337%

s

3,9199%



Literature








1 3,08%

-0,54% 0,30

2 -0,77%

3,30% 10,90

3 7,37%

-4,84% 23,44

4 1,90%

0,63% 0,40

5 -2,10%

4,63% 21,44

6 1,30%

1,23% 1,52

7 -2,09%

4,62% 21,34

8 -2,63%

5,17% 26,68

9 5,12%

-2,58% 6,66

10 3,92%

-1,38% 1,92

11 6,61%

-4,08% 16,61

12 8,68%

-6,15% 37,83

Σ 30,40% -

169,02

m

2,5337%

s

3,9199%



Literature








1 3,08%

-0,54% 0,30

2 -0,77%

3,30% 10,90

3 7,37%

-4,84% 23,44

4 1,90%

0,63% 0,40

5 -2,10%

4,63% 21,44

6 1,30%

1,23% 1,52

7 -2,09%

4,62% 21,34

8 -2,63%

5,17% 26,68

9 5,12%

-2,58% 6,66

10 3,92%

-1,38% 1,92

11 6,61%

-4,08% 16,61

12 8,68%

-6,15% 37,83

Σ 30,40% -

169,02

m 2,5337% s

3,9199%



Literature








1 3,08% -0,54%

0,30

2 -0,77% 3,30%

10,90

3 7,37% -4,84%

23,44

4 1,90% 0,63%

0,40

5 -2,10% 4,63%

21,44

6 1,30% 1,23%

1,52

7 -2,09% 4,62%

21,34

8 -2,63% 5,17%

26,68

9 5,12% -2,58%

6,66

10 3,92% -1,38%

1,92

11 6,61% -4,08%

16,61

12 8,68% -6,15%

37,83

Σ 30,40% -

169,02

m 2,5337% s

3,9199%



Literature








1 3,08% -0,54% 0,302 -0,77% 3,30% 10,903 7,37% -4,84% 23,444 1,90% 0,63% 0,405 -2,10% 4,63% 21,446 1,30% 1,23% 1,527 -2,09% 4,62% 21,348 -2,63% 5,17% 26,689 5,12% -2,58% 6,66

10 3,92% -1,38% 1,9211 6,61% -4,08% 16,6112 8,68% -6,15% 37,83

Σ 30,40% -

169,02

m 2,5337% s

3,9199%



Literature








1 3,08% -0,54% 0,302 -0,77% 3,30% 10,903 7,37% -4,84% 23,444 1,90% 0,63% 0,405 -2,10% 4,63% 21,446 1,30% 1,23% 1,527 -2,09% 4,62% 21,348 -2,63% 5,17% 26,689 5,12% -2,58% 6,66

10 3,92% -1,38% 1,9211 6,61% -4,08% 16,6112 8,68% -6,15% 37,83

Σ 30,40% - 169,02m 2,5337% s

3,9199%



Literature








1 3,08% -0,54% 0,302 -0,77% 3,30% 10,903 7,37% -4,84% 23,444 1,90% 0,63% 0,405 -2,10% 4,63% 21,446 1,30% 1,23% 1,527 -2,09% 4,62% 21,348 -2,63% 5,17% 26,689 5,12% -2,58% 6,66

10 3,92% -1,38% 1,9211 6,61% -4,08% 16,6112 8,68% -6,15% 37,83

Σ 30,40% - 169,02m 2,5337% s 3,9199%



Literature







m 2,5337%s 3,9199%

m+s 6,4535%m-s -1,3862%

u 1,0645d 0,9861



Literature






Create the binomial price treeOptions call and put parameters

Option type

Call Put

Option price 45,00 45,00Term 2 month 2 monthUSD rate, % annual 1% 1%RUB rate, % annual 8,00% 8,00%USD rate, % monthly 0,08% 0,08%RUB rate, % monthly 0,67% 0,67%



Literature






The binomial price tree



Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽

Figure 6.1: The binomial price tree



Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽




Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽




Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽




Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽




Literature







t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = ₽

x3 = $ y3 = ₽

α = ₽

45,7658 ₽ z1 = ₽

x1 = $ y1 = ₽

α = ₽

42,3954 ₽ z2 = ₽

x2 = $ y2 = ₽

60,2065 ₽ zr = ₽

48,7193 ₽ z = ₽

45,1314 ₽ z = ₽

41,8077 ₽ z = ₽




Literature






The option value for each earlier node is found,starting at the penultimate time step, and workingback to the first node of the tree (the valuationdate) where the calculated result is the value ofthe option.The "arbitrage free" approach creates a positionthat has an identical value in either state – thecash flow in one period is therefore known, andarbitrage pricing is applicable.



Literature






The option value for each earlier node is found,starting at the penultimate time step, and workingback to the first node of the tree (the valuationdate) where the calculated result is the value ofthe option.The "arbitrage free" approach creates a positionthat has an identical value in either state – thecash flow in one period is therefore known, andarbitrage pricing is applicable.



Literature






In case of an option the equivalent positionconsists of some amount of the base and quotedcurrency (one long and the other short) which hasthe value identical to the option price at the eachmoment.Under the risk neutrality assumption, today’s fairprice of a derivative is equal to the expected valueof its future payoff discounted by the risk free rate.Therefore, expected value is calculated using theoption values from the later two nodes.



Literature






In case of an option the equivalent positionconsists of some amount of the base and quotedcurrency (one long and the other short) which hasthe value identical to the option price at the eachmoment.Under the risk neutrality assumption, today’s fairprice of a derivative is equal to the expected valueof its future payoff discounted by the risk free rate.Therefore, expected value is calculated using theoption values from the later two nodes.



Literature






The expected value is then discounted at r, the riskfree rate corresponding to the life of the option.Long position in one currency yields interestrevenueShort position in the other currency cause interestcostUsually the interest revenue/expenses arecalculated on the basis of the risk free rate (e.g.LIBOR).



Literature









Literature









Literature









Literature






Option value at earlier nodes calculationexample

z1 = 45,7658 · x1 + y1

3,7193 = 48,7193 · x1 · (1 + rUSDn ) + y1 · (1 + rRUB

n )

0,1314 = 45,1314 · x1 · (1 + rUSDn ) + y1(1 + · rRUB

n )

z1 – the option value at each intermediate node;x1 – base currency position amount, negative value meansshort position;y1 – quoted currency position amount, negative value meansshort position;rUSD , rRUB – risk free deposit/lending rate, in the base andquoted currency respectively, annualn - interest rate compounding frequency (number ofcompounding periods per year, e.g. 12 months).



Literature







z1 = 45,7658 · x1 + y1

3,7193 = 48,7193 · x1 · (1 + rUSDn ) + y1 · (1 + rRUB

n )

0,1314 = 45,1314 · x1 · (1 + rUSDn ) + y1(1 + · rRUB

n )




Literature







z1 = 45,7658 · x1 + y1

3,7193 = 48,7193 · x1 · (1 + rUSDn ) + y1 · (1 + rRUB

n )

0,1314 = 45,1314 · x1 · (1 + rUSDn ) + y1(1 + · rRUB

n )




Literature







z1 = 45,7658 · x1 + y1

3,7193 = 48,7193 · x1 · (1 + rUSDn ) + y1 · (1 + rRUB

n )

0,1314 = 45,1314 · x1 · (1 + rUSDn ) + y1(1 + · rRUB

n )




Literature






Call and put options pricing is the same. Thedifference is only in options pricing at the finalperiods.If exercise is permitted at the node, then themodel takes the greater of binomial and exercisevalue at the node.



Literature






Call and put options pricing is the same. Thedifference is only in options pricing at the finalperiods.If exercise is permitted at the node, then themodel takes the greater of binomial and exercisevalue at the node.



Literature






Call option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 0, 2803 ₽

x3 = $0, 294 y3 = −12, 3741 ₽

α = 0, 7658 ₽

45,7658 ₽ z1 = 1, 0257 ₽

x1 = $0, 999 y1 = −44, 7020 ₽

α = 0, 0000 ₽

42,3954 ₽ z2 = 0, 0328 ₽

x2 = $0, 039 y2 = −1, 6416 ₽

60,2065 ₽ zr = 15, 2065 ₽

48,7193 ₽ z = 3, 7193 ₽

45,1314 ₽ z = 0, 1314 ₽

41,8077 ₽ z = 0, 0000 ₽

Figure 6.2: Option call



Literature






Call option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 0, 2803 ₽

x3 = $0, 294 y3 = −12, 3741 ₽

α = 0, 7658 ₽

45,7658 ₽ z1 = 1, 0257 ₽

x1 = $0, 999 y1 = −44, 7020 ₽

α = 0, 0000 ₽

42,3954 ₽ z2 = 0, 0328 ₽

x2 = $0, 039 y2 = −1, 6416 ₽

60,2065 ₽ zr = 15, 2065 ₽

48,7193 ₽ z = 3, 7193 ₽

45,1314 ₽ z = 0, 1314 ₽

41,8077 ₽ z = 0, 0000 ₽




Literature






Call option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 0, 2803 ₽

x3 = $0, 294 y3 = −12, 3741 ₽

α = 0, 7658 ₽

45,7658 ₽ z1 = 1, 0257 ₽

x1 = $0, 999 y1 = −44, 7020 ₽

α = 0, 0000 ₽

42,3954 ₽ z2 = 0, 0328 ₽

x2 = $0, 039 y2 = −1, 6416 ₽

60,2065 ₽ zr = 15, 2065 ₽

48,7193 ₽ z = 3, 7193 ₽

45,1314 ₽ z = 0, 1314 ₽

41,8077 ₽ z = 0, 0000 ₽




Literature






Call option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 0, 2803 ₽

x3 = $0, 294 y3 = −12, 3741 ₽

α = 0, 7658 ₽

45,7658 ₽ z1 = 1, 0257 ₽

x1 = $0, 999 y1 = −44, 7020 ₽

α = 0, 0000 ₽

42,3954 ₽ z2 = 0, 0328 ₽

x2 = $0, 039 y2 = −1, 6416 ₽

60,2065 ₽ zr = 15, 2065 ₽

48,7193 ₽ z = 3, 7193 ₽

45,1314 ₽ z = 0, 1314 ₽

41,8077 ₽ z = 0, 0000 ₽




Literature






Call option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 0, 2803 ₽

x3 = $0, 294 y3 = −12, 3741 ₽

α = 0, 7658 ₽

45,7658 ₽ z1 = 1, 0257 ₽

x1 = $0, 999 y1 = −44, 7020 ₽

α = 0, 0000 ₽

42,3954 ₽ z2 = 0, 0328 ₽

x2 = $0, 039 y2 = −1, 6416 ₽

60,2065 ₽ zr = 15, 2065 ₽

48,7193 ₽ z = 3, 7193 ₽

45,1314 ₽ z = 0, 1314 ₽

41,8077 ₽ z = 0, 0000 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽

Figure 6.3: Option put



Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Put option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = 1.9375 ₽

x3 =−$0.772

y3 = 35.1334 ₽

α = 0 ₽

45,7658 ₽ z1 = 0 ₽

x1 = $0 y1 = 0 ₽

α = 2.6046 ₽

42,3954 ₽ z2 = 2.6046 ₽

x2 =−$0.960

y2 = 43.0604 ₽

48,7193 ₽ z = 0 ₽

45,1314 ₽ z = 0 ₽

60,2065 ₽ zr = 0 ₽

41,8077 ₽ z = 3.1923 ₽




Literature






Binary options pricingBinary options parameters

Option type

One touch No touch

Barrier price 48,00 42,50Payoff $1 000 $1 000Term 2 months 2 monthsUSD rate, % annual 1% 1%RUB rate, % annual 8,00% 8,00%USD rate, % monthly 0,08% 0,08%RUB rate, % monthly 0,67% 0,67%



Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0

Figure 6.4: One touch option



Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






One touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $62

x3 = $3179 y3 = −134028 ₽

45,7658 ₽ z1 = $249

x1 = $12745 y1 = −571865 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0

Figure 6.5: No touch option



Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






No touch option

t =01.10.2014

t =01.11.2014

t =01.12.2014

42,9913 ₽ z3 = $249

x3 = $12745 y3 = −537197 ₽

45,7658 ₽ z1 = $1000

x1 = $1000 y1 = −45766 ₽

42,3954 ₽ z2 = $0

x2 = $0 y2 = 0 ₽

60,2065 ₽ zr = $1000

48,7193 ₽ z = $1000

45,1314 ₽ z = $0

41,8077 ₽ z = $0




Literature






General one period model

S C

u · S Cu

d · S Cd

RE ROt = Tt = 0

Figure 6.6: General one period model

whereS - undelying asset current price;E - options execution price.

Cu =

u · S − E, for u · S > E0, for u · S ≤ E

(6.1)

Cd =

d · S − E, for d · S > E0, for d · S ≤ E

(6.2)



Literature






System of equations for one period modeland its solution

C = S · x + yCu = u · S · x · rUSD + y · rRUB

Cd = d · S · x · rUSD + y · rRUB

(6.3)

x =Cu − Cd

(u − d) · S · rUSDy =

u · Cd − d · Cu

(u − d) · rRUB(6.4)

C = S · x + y (6.5)

wherex , y - position amounts in dollars and rouble, respectively;rUSD , rRUB - deposit/lending rates for time period T in dollars androubles, respectively.

Documents

Borochkin A. A. International Finance. Lectures. Part 1