03-PS5-OP_sol - MIT Sloan School of Management J. Wang...

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Unformatted text preview: MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 5: Options Not required to hand it 1. (a) Using the put-call parity, C = P + S - PV(K) = 5 + 94 - 80*.91 = 26.2 (b) He is wrong. The put-call parity relies on the no-arbitrage argument, and if it is violated you can make risk-free profit in the market. Since the call is overpriced, you write the call and buy a replicating portfolio, which involves buying one unit of stock, buying a put of strike 80 and borrowing PV(80) = 72.8. This will costs your 26.2, but you get 30 from writing the call. Now you have a net cashflow of 3.8, and you have a net cashflow of zero in the future. 2. (a) The intrinsic value is just max(S-K,0) (b) The value of a call increases with maturity. Since the intrinsic value does not change, time value must increase. (c) Case 1: Call in in the money. Notice that when strike price increase, call price goes up less than 1-for-1. However, the intrinsic value goes up 1-for-1. Therefore the time value of the option decreases. Case 2: Call in out-of-the money. Now if strike price goes up, call value goes up but intrinsic value stays at zero. Therefore time value increases. This example tells you that the industry definition of time value is quite artificial. (d) If the two companies have different volatility, the one with higher volatility will have a higher option price, and hence higher time-value. The only thing that is the same is the intrinsic value. 3. (a) p = 5%- (- 5)% 15%- (- 5)% = 0 . 5 (b) The option is in the money only if stock goes down in all next 3 years. Therefore, P = (100- 100 * . 95 3 ) * p 3 1 . 05 3 = 1 . 5401 Constructing the replicating portfolio: The option price evolves according to the binomial table: t = 0 1 2 3 1.5401 3.2341 6.7912 14.2625 1 At time 0, you want to short some stock so that you have a payoff of 0 if stock goes...
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.

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03-PS5-OP_sol - MIT Sloan School of Management J. Wang...

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