Lecture 1

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Derivative SecuritiesLecture 1 Introduction to Derivatives

Nicholas ChenNicholas Chen, ICMA Centre1

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IntroductionA little bit about myselfWhat I am sharing with youKnowledge in finance Applying financial valuation principles to your personal life

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Introduction (Cont)Why is it so hard to make decisionsUncertain consequences Can I wait to make decisions later on?Yes, there is a fee for you to delay your decision-making.In finance, everything, including the right of making decision, will be priced.Nicholas Chen, ICMA Centre3

Rent a Flat in Town CentreThe first decision I need to make is to rent

The deposit 300 is the price to have ________ to make decision later on. Nicholas Chen, ICMA Centre4To Rent: 800 300 = 500Not to Rent: Lose 300Deposit : 300

ObjectivesDescribe and characterize derivatives and marketsEvaluate and apply pricing and trading methodsPerform analysis of financial derivatives dataConstruct simple spreadsheets for derivatives pricing and trading

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MaterialsRequired textbookOptions, Futures and Other Derivatives (Hull, 8th ed)The 7th Edition is ok. Recommended Financial Times and WSJ

Course OperationAttendanceWork on Assignments on your ownFive seminars (where Assignments will not be collected)Casey Chen, [email protected] option pricing and trading sessionsTom Markham, [email protected] hoursMonday 3 pm 5pm

AssessmentOne multiple-choice in-class test (20%)Four trading sessions (10%)One 1.5 hour final examination (70%)

Helpful hintsSpend one hour each dayPractice is the keySpeak up in the class

Todays Outline

What are derivatives?Forward contractsFutures contractsOptions ContractsTrading types Arbitrage and futures pricingNicholas Chen, ICMA Centre10

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1. What are derivatives?

an instrument whose value depends on the values of other, more basic, underlyingvariables

The underlying variables are generally traded assets, e.g. stocks, indices, commodities, exchange rates or fixed income securities. But they can be any variable, e.g. the weather.

The dependence can be of many types.Nicholas Chen, ICMA Centre11

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Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

1.12Underlying Assets: CommoditiesCategories of commodities with exchange-traded derivatives:

Energy

Metals

Grains and Oil seeds

Livestock and Meat

Food and Fiber

Derivative Securities121. Introduction 1.2 Underlying AssetsActivity: Provide newspaper and list contracts within each categoryFor analysing many derivatives it is important to understand how the underlying asset moves over time. Grains and Oil seeds: Maize, Wheat, Rubber, Palm Oil, SoyabeansLivestock and Meat: Not much trading in Europe, Pork belliesFood and Fibers: Coffee, Cocoa, Sugar, CottonEnergy: Oil, Gas, Heavy Fuel, Naphtha, Jet fuel, DieselMetals: Alum, Copper, Lead, Nickel, Tin, Zinc, Gold, Silver

Popular US common stock indexes with associated exchange-traded derivatives: S&P 500 Index Dow Jones Industrial Average FTSE Eurofirst 300

The S&P 500 Index, widely diversified across US industries, comprises 500 stocks, for the most part traded on the NYSE. Typically, it includes the most important stocks in their respective industries. The Index is value-weighted, and a continuous daily price series exists since 1928.Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

1.13Underlying Assets: Common Stocks and Indexes

Derivative Securities13Activity: provide newspaper and list contracts within each categoryUS Indices: S&P 500 Index and its variations Mini, S&P 100, etc.European Indices:FTSE Eurotop 300, DJ Euro Stoxx 50Dow Jones Industrial Average 30 Blue Chip corporations; computed since 1896.OriginallyJust like the percentage change of a portfolio with one share in each of the 30 stocks in the index.Price-weighted average.

NowDJIA no longer equals the average price of the 30 stocks because the averaging procedure has been adjusted for stock splits , stock dividends (of more than 10%) or when one of the stock component is replaced by another.

Value weighted index, more weight to companies with greater market value. To better reflect the change in market value.

Popular fixed income securities:

US Treasury billsEurodollarsUS Treasury notes/bonds Mortgages

Real world candidates for cashDerivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

1.14Fixed Income Securities

Derivative Securities14T-bills : securities guaranteed by the US government, zero coupon bonds (pay no coupon and provide payment of the principal at maturity). Maturity of 1 year or less.

Repos : sale of US Gov/EU Gov fixed income securities with the agreement to buy them back in the future.short-term (1-day) collateralized borrowing and lending

Eurodollars : deposits of us dollars in a bank outside the Usa. The Centre for this market is London and the London Interbank offer rate (LIBOR) is the standard Eurodollar quoted interest rate.

US t-notes : t-notes with maturity of 10 years or lessUS t-bonds : with initial maturity of more than 10 years; provide coupon payments

Types of derivativesForwards: agreements to buy/sell an underlying in the future at a certain price agreed today over the counter

Futures: same as forwards, except that they are standardized and settled daily in exchanges

Options (call/put): contracts offered at a fee (or premium) that give the right to buy/sell an underlying in the future (same as futures but no obligation)

Structured products: contracts with non-standard payoff (e.g. convertible bonds, asset-backed securities)Nicholas Chen, ICMA Centre15

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2. Forward contractsForward = agreement to buy/sell an asset at a certain future time for a certain price agreed today they require no fee!

Spot contract = agreement to buy or sell an asset today

Specifications:UnderlyingType of agreement: buy/sellTime of deliveryDelivery priceSizeNicholas Chen, ICMA Centre16

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Forward contractstraded over-the-counterpersonalizedsettled at the end of the contract they involve some credit riskhave zero value at the time of agreement, so no fee is exchanged Forward price = the price that makes the value of forward contract exactly zero.Terminology:Long position: the buyerShort position: the sellerNicholas Chen, ICMA Centre17

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Forward (and Futures) Contracts

October , 2011December, 2011

Ill buy your house in Julyfor $350,000.Youve got a deal.

Nothing is exchanged now.

Thanks for the house. Thanks for the $350,000.Trade occurs in the future.

Derivative Securities181. Introduction 1.3 Types of Derivatives

Specification of the above exampleSpecifications of a long forward contract:Underlying: _____________Type of agreement:_____________Time of delivery: ______________Price: ______________Size: ______________

Nicholas Chen, ICMA Centre19

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Position in forward contractsThe price of a 6-month forward contract of gold is $400.

What does Long such a forward contract mean?

You commit to __ gold at the price of $__ in __ months.

Suppose the spot price is $450 in 6 months, will you make any profit?

Profit = ______________The profit at maturity is ST K, where is the spot price ST is the spot price and K is the delivery price or the forward price when you enter into the contract.


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Profit from a Long Forward Position (K= delivery price=forward price at time contract is entered into)Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201221

ProfitPrice of Underlying at Maturity, STK

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Profit from a Short Forward Position (K= delivery price=forward price at time contract is entered into)Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201222

ProfitPrice of underlying at Maturity, ST

K

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3. Futures contractsSame as forward contracts, except:

traded on exchanges

standardized

settled daily almost no credit risk involved they require margins


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Exchanges

Chicago Board of Trade

Chicago Mercantile Exchange

LIFFE (London)

Eurex (Europe)

TIFFE (Tokyo)Nicholas Chen, ICMA Centre24

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DeliveryMost futures contracts are closed out before maturity by entering into an offsetting position

Otherwise they are settled by delivering the underlying assets (when there are alternatives then the counterparty with the short position is making the choice about delivery conditions)

Some contracts (e.g. those written on indices or FX rates) are settled in cashNicholas Chen, ICMA Centre25

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TerminologySettlement price: the price used in the last trade of the day (________________)

Open interest: the number of contracts outstanding a new trade can increase/decrease open interest

Trading volume: the total number of trades during the day a new trade always increases volumeNicholas Chen, ICMA Centre26

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Margins

Cash or security deposited by an investor with his broker that helps avoid contract defaults

Settled daily (marked to market)

Minimize the possibility of a loss due to the default of a counterparty

Types: initial and maintenance

Clearinghouse: holds the margin accountsNicholas Chen, ICMA Centre27

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Margins - exampleAn institution takes a long position in a 6-month futures contract on stock A with the futures price being 100. Now the stock trades at 110. Contracts are written on 100 stocks.

The initial margin requirement is 2,000 per contract.

The maintenance margin is 1,000 per contract.

If an investor cannot pay the required margin then his contract will be closed no credit riskNicholas Chen, ICMA Centre28

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Margins - example


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Margins - example


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Margins - example


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Margins - example


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Forward vs. futures contractsNicholas Chen, ICMA Centre33

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Forward vs. futures contractsForward contract is similar to the rental from a private party. Futures contract is similar to the rental from a letting agent, which can regarded as an exchange. Nicholas Chen, ICMA Centre34

Nicholas Chen, ICMA Centre, 20114. Options contract offered at a fee (price) thatgives the right to buy/sell an assetin the future at a pre-defined price

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Nicholas Chen, ICMA Centre, 2011TerminologyCall option gives the right to buyPut option gives the right to sell

Long the option the one who has the right he pays the feeShort the option the one who has the obligation he receives the fee

European option can be exercised on a specific dateAmerican option can be exercised until a specific date

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A bad decision makerI like the house. However, I have not decided I might change my mind in December.

Can you hold it for me?Nicholas Chen, ICMA Centre37


(European) Call Options

If you pay me $50,000 extra now, its a deal.

Ill buy your house in December for $350,000, if I want to then.

October

Housing Prices FallIve decided not to buy. Thats OK. But I get to keep the $50,000.December

Thanks for the house. Thanks for the $350,000.

Housing Prices RiseThe right (not obligation) to buy an asset a certain time


A even worse decision makerI like the house. However, I have not decided I might Change my mind in the future. But I do not even know when I will change my mind?Can you still hold it for me?Nicholas Chen, ICMA Centre39


American Call Options

If you pay me $60,000 extra now, its a deal.

Ill buy your house before December for $350,000, if I want to then.

October

Housing Prices FallIve decided not to buy. Thats OK. But I get to keep the $60,000.November

Thanks for the house. Thanks for the $350,000.

Housing Prices RiseThe right (not obligation) to buy an asset whenever you change your mind before the expiration day.


5. TradersTypes of traders:

HedgersRequire investmentReduce risk by ocking in the prices.

Speculators very risky!Require investmentIncrease risk by taking directional positions

ArbitrageoursRequire no initial investmentsTake zero riskWhat rate of return do arbitrageours expect to receive?Nicholas Chen, ICMA Centre41

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Hedging example A British company A will need to pay 10 mil in 6 months. Company A will hedge this obligation with a long position in a forward contract, agreeing to buy 10 mil in 6 months at a specified forward rate 0.91 /.

No matter how much the exchange rate will be, company A will have to buy the euro at the pre-specified rate.

If the exchange rate will be 0.93 /, then company A made a good deal, If the exchange rate will be less than 0.91 /, then company A made a loss.Nicholas Chen, ICMA Centre42

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Hedging ExerciseA US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a ___ position in a forward contract.


Speculation Example (pages 10-11)

An investor with $4,000 to invest feels that Amazon.coms stock price will increase over the next 2 months. The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2

What are the alternative strategies? Strategy 1: buy $4000 worth of stock Strategy 2: buy $4000 worth of optionsDerivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

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Derivative Securities44

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Strategy 1: buy $4000 worth of stock 4000/40 = 100 sharesStrategy 2: buy $4000 worth of options 4000/2 = 2000 options (20 Dec contracts)

Possible outcomes in Dec:Profit/LossAMZN share price = $70AMZN share price = $30Strategy 1:(70-40)*100 = 3,000(30-40)*100 = -1,000Strategy 2:(70-45)*2000-4,000=46,0000-4,000 = -4,000

Strategy 1: Buy StockStrategy 1: buy $4000 worth of stock 4000/40 = 100 shares

Possible outcomes in Dec:If AMZN share price = $70Gain ________________If AMZN share price = $30 lose _______________Nicholas Chen, ICMA Centre45

Strategy 2: Buy optionsStrategy 2: buy $4000 worth of options 4000/2 = 2000 options (20 Dec contracts)

If AMZN share price = $70Gain __________________If AMZN share price = $30 lose _________________


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Arbitrage ExampleGold: An Arbitrage Opportunity?Suppose that:The spot price of gold is US$390The quoted 1-year futures price of gold is US$425The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity? Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

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To have gold 1 year from now I can use one of the following two alternative strategiesBuy gold now, store it until due date (cost of borrowing, no cost of storing)Take a long position in futures contract which does not involve any cash outflow now except for margin payments

=> futures price too HIGH , yes there is an Arbitrage opportunityBorrow money, buy gold and carry it to maturity of the futures contract$390---> 390* e0.05x1 = 410$390---> 390* (1+0.05) = 409.5short 1 futures contractreceive $425in 1 year

(cost to pay back loan =390e0.05*T=410)< (payoff = 425)

risk free profit of 15 (15.5).

Arbitrage Example (cont)Futures price too __________ , yes there is an Arbitrage opportunity

TodayBorrow money, buy gold and carry it to maturity of the futures contract$390---> 390* e0.05x1 = 410short 1 futures contractreceive $425 in 1 year

One year laterClose the futures contract by selling the gold at 425cost to pay back loan =390e0.05*T=410

risk free profit of 425- 410 = 15Nicholas Chen, ICMA Centre48

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Arbitrage ExerciseSuppose that:The spot price of gold is US$390The quoted 1-year futures price of gold is US$390The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

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Futures price too LOW take a long position in futures contract and sell spot (if owned)

receive 390, deposit in bank at 5% interest, it will grow to 410 (409.5 with yearly compounding)at maturity pay 390 and receive gold, saving $20 (19.5) per contract

price of spot will decrease and price of futures will increase

Arbitrage opportunity will cease when F=SerT (no storage cost and no transaction costs)F=S(1+r)T

Arbitrage Exercise (Cont)Futures price is ____Todaytake a long position in futures contract Short sell gold to receive $390 (borrow the gold and sell it to the market)deposit $390 in bank at 5% interestat maturityReceive $410 (390* e0.05x1 = 410) from the depositbuy gold at $390 to close out the futures positionreturn the gold to the lender to close the short sell position

risk free profit = _____________ = $20 per contractNicholas Chen, ICMA Centre50

The Futures Price of Gold If the spot price of gold is S & the futures price for a contract deliverable in T years is F, then F = S e rT or F = S (1+r )T where r is the 1-year (domestic currency) risk-free rate of interest.In our examples, S=390, T=1, and r=0.05 so thatF = ___________________Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

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Futures price = opportunity cost from investing an amount S in gold and forgoing interests + cost of storing gold (in this simple example is zero)

Key Q: Why Use Risk-free Rate?Because forward and futures price is fixed in the contract, ________ risk.Nicholas Chen, ICMA Centre52

Exercise Problem of Futures PricingSuppose that:The spot price of oil is US$19The 1-year US$ interest rate is 5% per annum

What is the price of oil futures contract?Derivative Securities - INVEST II, Spring 2005, Dr. Alfonso Dufour

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$25: futures price too high borrow 19, buy spot, and short futuresat maturity pay back loan + storage costs 19*(1+0.05+0.02) = 20.33 , deliver oil and receive $25 for a risk free profit of $4.67$16: futures price too low owners of oil would be willing to take advantage of the following arbitrage opportunitysell spot and go long futuresget 19 now, invest in bank at 5% interest rate

The Futures Price of Oil

In our examples, S=19, T=1 and r=0.05 so thatF = 19(1+0.05) = 19.95


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No arbitrage futures price of oil

Convergence of futures to spot price (when T 0)


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Lecture 1