DM4-Option strategies

DM4-Option strategies - Option Styles European option –...

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Unformatted text preview: Option Styles European option – Holder can exercise the option only on the expiration date American option – Holder can exercise the option anytime during the life of the option Bermuda option – Holder can exercise the option during certain prespecified dates before or at the expiration date Call Put Buy ↑ ↓ Short Forward Long Call Write ↓ ↑ Long Forward Short Call Payoff Floor – own + buy put Cap – short + buy call Covered Call – stock + write call = write put Covered Put – short +write put = write call Profit Price at Maturity Cash-and-Carry – buy asset + short forward contract Synthetic Forward – a combination of a long call and a short put with the same expiration date and strike price Long Put Short Put Fo,T = no arbitrage forward price Call(K,T) = premium of call Put-Call Parity Derivative Position Long Forward Short Forward Long Call Short Call Long Put Short Put Maximum Loss Maximum Gain Strategy Payoff Unlimited Position wrt Underlying Asset Long(buy) -Forward Price Guaranteed price PT-K Unlimited Forward Price Short(sell) Guaranteed price K-PT -FV(Premium) Unlimited -FV(Premium) FV(Premium) – Strike Price Unlimited FV(Premium) Strike Price – FV(Premium) FV(Premium) Long(buy) Short(sell) Short(sell) Long(buy) Insures against high price Sells insurance against high price Insures against low price Sells insurance against low price max{0,PT-K} -max{0,PT-K} max{0,K-PT} -max{0,K-PT} (Buy index) + (Buy put option with strike K) = (Buy call option with strike K) + (Buy zero-coupon bond with par value K) (Short index) + (Buy call option with strike K) = (Buy put option with strike K) + (Take loan with maturity of K) Spread Strategy Creating a position consisting of only calls or only puts, in which some options are purchased and some are sold Bull Spread o Investor speculates stock price will increase o Bull Call Buy call with strike price K1, sell call with strike price K2>K1 and same expiration date o Bull Put Buy put with strike price K1, sell put with strike price K2>K1 and same expiration date o Two profits are equivalent (Buy K1 call) + (Sell K2 call) = (Buy K1 put) + (Sell K2 put) o Profit function Bear Spread o Investor speculates stock price will decrease o Exact opposite of a bull spread o Bear Call Sell K1 call, buy K2 call, where 0<K1<K2 o Bear Put Sell K1 put, buy K2 put, where 1<K1<K2 Long Box Spread Bull Call Spread Bear Put Spread Synthetic Long Forward Buy call at K1 Sell put at K1 Synthetic Short Forward Sell call at K2 Buy put at K2 Regardless of spot price at expiration, the box spread guarantees a cash flow of K2-K1 in the future. Net premium of acquiring this position is PV(K2-K1) If K1<K2, then lending money Invest PV(K2-K1), get K2-K1 If K1>K2, then borrow money Get PV(K1-K2), pay K1-K2 Butterfly Spread An insured written straddle Let K1<K2<K3 o Written straddle Sell K2 call, sell K2 put o Long strangle Buy K1 call, buy K3 put Profit o Let F o Profit Payoff K2-K1 K2-K1-FV[… PT PT K1 K2 -FV[… Asymmetric Butterfly Spread Collar Used to speculate on the decrease of the price of an asset Buy K1-strike at-the-money put Sell K2-strike out-of-the-money call K2>K1 K2-K1 = collar width Profit Function Collared Stock Collars can be used to insure assets we own Buy index Buy at-the-money K1 put Buy out-of-the-money K2 call K1<K2 Profit Function Zero-cost Collar A collar with zero cost at time 0, i.e. zero net premium Straddle A bet on market volatility Buy K-strike call Buy K-strike put Strangle A straddle with lower premium cost Buy K1-strike call Buy K2 strike put K1<K2 Profit Function Profit Function Equity-linked CD (ELCD) Can financially engineer an equivalent by Buy zero-coupon bond at discount Use the difference to pay for an at-the-money call option Prepaid Forward Contracts on Stock Let FP0,T denote the prepaid forward price for an asset bought at time 0 and delivered at time T If no dividends, then FP0,T = S0, otherwise arbitrage opportunities exist If discrete dividends, then o If continuous dividends, then o Let δ=yield rate, then the and 1 share at time 0 grows to eδT shares at time T Forward Contracts Discrete dividends o Continuous dividends o Forward premium = F0,T / S0 The annualized forward premium α satisfies o If no dividends, then α=r If continuous dividends, then α=r-δ Financial Engineering of Synthetics (Forward) = (Stock) – (Zero-coupon bond) o Buy e-δT shares of stock o Borrow S0e-δT to pay for stock o Payoff = PT – F0,T (Stock) = (Forward) + (Zero-coupon bond) o Buy forward with price F0,T = S0e(r-δ)T o Lend S0e-δT o Payoff = PT (Zero-coupon bond) = (Stock) – (Forward) o Buy e-δT shares o Short one forward contract with price F0,T o Payoff = F0,T o If the rate of return on the synthetic bond is i, then S0e(i-δ)T = F0,T or Implied repo rate ...
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