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MSA 736 Fixed Income & Derivatives II

MSA 736 Fixed Income & Derivatives II. Chapters 7 Option Strategies. Calls and Stock: the Covered Call. Own the stock, sell a call Profit equation: P = N S (S T - S 0 ) + N C [Max(0,S T - X) - C] given N S > 0, N C < 0, N S = -N C . With N S = 1, N C = -1,

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MSA 736 Fixed Income & Derivatives II

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  1. MSA 736Fixed Income & Derivatives II Chapters 7 Option Strategies

  2. Calls and Stock: the Covered Call • Own the stock, sell a call • Profit equation: P = NS(ST - S0) + NC[Max(0,ST - X) - C] given NS > 0, NC < 0, NS = -NC. With NS = 1, NC = -1, • P = ST - S0 + C if ST£ X • P = X - S0 + C if ST > X • Give away upside above strike for premium today • Maximum profit = X - S0 + C, minimum = -S0 + C • Breakeven stock price found by setting profit equation to zero and solving: ST* = S0 - C

  3. Puts and Stock: the Protective Put • Own the stock, buy a put • Profit equation: P = NS(ST - S0) + NP[Max(0,X - ST) - P] given NS > 0, NP > 0, NS = NP. With NS = 1, NP = 1, • P = ST - S0 - P if ST³ X • P = X - S0 - P if ST < X • Buy a put – profit below strike price • Maximum profit = , minimum = X - S0 - P • Breakeven stock price found by setting profit equation to zero and solving: ST* = P + S0 • Like insurance policy

  4. Bull (Call) Spread • The buyer of the spread purchases a call option with a low exercise price, XL at price CL • Subsidizes the purchase price of that call by selling a call at CH with a higher exercise price, XH • Note: CH < CL, so there is a cost Continued →

  5. Summary of Bull (Call) Spread Payoffs • Profit: max(0, S – XL) – max(0, S – XH) – CL+CH • Maximum profit = XH – XL – CL +CH • Maximum loss = CL – CH • Breakeven price = XL + CL – CH

  6. Bear Put Spread • Bear Spreads • Purchase put with high strike price and sell put with low strike price • Buy put with strike X2, sell put with strike X1.

  7. Bear Put Spread Summary • Profit: max(0, XH– S) – max(0, XL– S) – PH+PL • Maximum profit: XH –XL – PH + PL • Maximum loss: PH – PL • Breakeven price: XH – PH + PL

  8. Collar • A collar is the combination of a protective put and covered call • Often, the owner of the underlying asset buys a protective put and then sells a call to pay for the put • If the premiums of the two are equal, this is called a zero-cost collar Continued →

  9. Protective Collar • Collars • Buy stock, buy put with strike X1, sell call with higher strike X2. • In short, buy a put and finance the purchase by selling a call with higher strike. • A common type of collar is what is often referred to as a zero-cost collar. The call strike is set such that the call premium offsets the put premium so that there is no initial outlay for the options.

  10. Collar (Cont.) • Profit = max(0, XL – ST) – max(0, ST – XH) + ST – S0 – P0 + C0 • Maximum profit = XH – S0 • Maximum loss = S0 – XL • Breakeven price = S0

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