DERIVATIVES

Introduction Cash market strategies are limited Long (asset is expected to appreciate) Short (asset is expected to depreciate) Alternative views Appreciation within a range Depreciation within a range Appreciation outside a range Depreciation outside a range Appreciation with protection against depreciation …..

Derivatives Securities whose price is derived from other assets Payoff depends on the value of other securities Examples Futures futures VIX futures Call options Put options Digital options Collar ……..

Option Contract Call 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 Assets Equity Commodity Foreign Exchange Indexes S&P Volatility VIX Futures Interest rate Cap Floor Collar Corridor Swaps (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 Stock Option is a leveraged position in stock Stock price=$90 Premium of one year call with strike of $90 = $10 Interest rate = 2% Funds to invest = $9,000 Investment 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 Portfolios Values 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 00$4,500$9,000$13,500$18,000 C) 100 Call + Deposit $8160 $8,600$9,160$9,660$10,160

Performance of Portfolios Values 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% -50%0%50%100% C) 100 Call + Deposit -9.33% -3.78%1.78%7.33%12.89%

Option Strategies Combination 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

Collar Long Stock, Short Call, Long Put with different strikes

Collar Payoff Long Stock, Short Call, Long Put with different strikes

Put-Call-Parity C = P + S – PV(X)