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Session+25+_1_ - 1 MECHANICS OF OPTIONS MARKETS Options...

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Unformatted text preview: 1 MECHANICS OF OPTIONS MARKETS Options, Futures, and Other Derivatives, 7th Ed., John C. Hull (2008): Chapter 9-10 Notation 2 c : European call option price p : European put option price S0 : Stock price today American Call option price P : American Put option price ST :Stock price at option maturity D : Present value of dividends during option’s life r : Risk‐free rate for maturity T with cont comp K : Strike price T : Life of option C : : Volatility of stock price 3 The Impact of Dividends on Lower Bounds to Option Prices c S 0 D Ke rT p D Ke For the Put-Call Parity: European options; D > 0 c + D + Ke -rT = p + S0 rT S0 Early Exercise 4 Usually there is some chance that an American option will be exercised early An exception is an American call on a non‐dividend paying stock This should never be exercised early An Extreme Situation 5 For an American call option: S0 = 100; T = 0.25; K = 60; D = 0 Should you exercise immediately? What should you do if you do not feel that the stock is worth holding for the next 3 months? you want to hold the stock for the next 3 months? You will likely not exercise as: No income is sacrificed Payment of the strike price is delayed Holding the call provides insurance against stock price falling below strike price 6 Should Puts Be Exercised Early ? Are there any advantages to exercising an American put when S0 = 60; T = 0.25; r=10% K = 100; D = 0 Since K‐ S> Ke‐rT –S for all values of K and S, it may be worth forgoing the insurance a put can provide if the put is sufficiently deep in the money Types of Strategies 7 Take a position in the option and the underlying Take a position in 2 or more options of the same type (A spread) Combination: Take a position in a mixture of calls & puts (A combination) 7 Positions in an Option & the Underlying 8 A covered call Payoff Payoff K K ST ST (a) (b) A protective put Payoff Payoff K K ST (c) ST (d) 8 Bull Spread Using Calls 9 Profit ST K1 K2 9 Bear Spread Using Puts 10 Profit K1 K2 ST 10 Box Spread 11 A combination of a bull call spread and a bear put spread If all options are European a box spread is worth the present value of the difference between the strike prices Stock Price Payoff from Bull Call Payoff from Bear Put Spread Spread Total Payoff ST ≤ K 0 K2 – K1 K2 – K1 K1 < ST< K2 ST –K1 K2 – ST K2 – K1 ST ≥ K K2 –K1 0 K2 – K1 11 Butterfly Spread Using Calls 12 Assume K2 = 1/2(K1 + K3) Stock Price Payoff from first long call (K1) ST ≤ K1 0 0 0 0 K1 < ST < K2 ST –K1 0 0 ST –K1 K2 <ST ≤ K3 ST –K1 0 ‐2(ST –K2) K3 – ST ST ≥ K3 ST –K1 ST –K3 ‐2(ST –K2) 0 Payoff from Payoff from second long call two short calls (K3) (K2) Total Payoff Butterfly Spread Using Calls 13 Profit K1 K2 K3 ST 13 A Straddle Combination 14 Profit K ST 14 Strangle 15 Payoff K1 K2 ST 15 ...
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