DERIVATIVES

IntroductionCash market strategies are limited

Long (asset is expected to appreciate)Short (asset is expected to depreciate)

Alternative viewsAppreciation within a rangeDepreciation within a rangeAppreciation outside a range Depreciation outside a rangeAppreciation with protection against

depreciation …..

DerivativesSecurities whose price is derived from other

assetsPayoff depends on the value of other securitiesExamples

Futures futuresVIX futuresCall optionsPut optionsDigital optionsCollar……..

Option ContractCall option gives the buyer the right (not

the obligation) to buy an asset for a certain price before some specified time

Put option gives the buyer the right (not the obligation) sell an asset for a certain price before some specified time

Exchange Traded Over The Counter (OTC)

Underlying AssetsEquityCommodityForeign Exchange Indexes

S&PVolatility VIX

FuturesInterest rate

CapFloorCollarCorridorSwaps (flat forward)

Payoff Profile & Profit of Long Call

Payoff of a long Call option at expiration with strike of S with X the price of underlying = Max ( 0, X –S )

$ payoff Profit

& Loss (P&L)

S Asset Price

Payoff Profile & Profit of Short Call

Payoff of a short Call option at expiration with strike of S with X the price of underlying = Min ( 0, S – X )

$ S Asset Price Payoff Profit & Loss (P&L)

Payoff Profile & Profit of Long Put

Payoff of a long Put option at expiration with strike of S with X the price of underlying = Max ( 0, S - X )

$ payoff

S Asset Price

Profit & Loss (P&L)

Payoff Profile & Profit of Short Put

Payoff of a short Put option at expiration with strike of S with X the price of underlying = Min ( 0, X – S )

$ Profit & Loss (P&L) S Asset Price Payoff

Option vs StockOption is a leveraged position in stock Stock price=$90Premium of one year call with strike of $90 =

$10Interest rate = 2%Funds to invest = $9,000Investment Alternatives

Portfolio A: Buy 100 shares of stock (unlevered position) for $9,000

Portfolio B: Buy 900 calls (highly levered position)Portfolio C: Purchase 100 calls, invest remaining

$8,000 at 2%

Values of PortfoliosValues of portfolios for different stock

price in one year

Portfolio

$85 $90 $95 $100 $105 $110

A) 100 shares

$8500 $9000 $9500 $10,000 $10,500 $11,000

B)900 Calls

0 0 $4,500 $9,000 $13,500 $18,000

C)100 Call + Deposit

$8160 $8160 $8,600 $9,160 $9,660 $10,160

Performance of PortfoliosValues of portfolios for different stock

price in one year

Portfolio

$85 $90 $95 $100 $105 $110

A) 100 shares

-5.56% 0.00% 5.56% 11.11% 16.67% 22.22%

B)900 Calls

-100% -100% -50% 0% 50% 100%

C)100 Call + Deposit

-9.33% -9.33% -3.78% 1.78% 7.33% 12.89%

Option StrategiesCombination of options can be used to

achieve certain investment objectives are not available using the cash market

Protective Put Long Stock, Long Put Stock

Put Payoff

Performance of Protective Put + Stock

Buying insurance on stock position Stock

Put Payoff

Covered Call Long Stock, Short Call Stock

Short Call Payoff

Performance of Covered Call Long Stock, Short Call Stock

Put Payoff

Long Straddle Long Call, Long Put with same strike

Long Straddle Payoff Long Call, Long Put with same strike

Short Straddle Short Call, Short Put with same strike

Short Straddle Payoff Short Call, Short Put with same strike

Long Strangle Long Call, Long Put with different strikes

Long Strangle Payoff Long Call, Long Put with different strikes

Short Strangle Short Call, Short Put with different strikes

Short Straddle Payoff Short Call, Short Put with different strikes

CollarLong Stock, Short Call, Long Put with different

strikes

Collar PayoffLong Stock, Short Call, Long Put with different

strikes

Put-Call-Parity

C = P + S – PV(X)