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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Case 2 solutions Solutions to Rinconete: payoff tables and payoff diagrams Part A 1. In order to answer this question we simply have to work out when it is optimal to exercise the options, and then add the payoffs from each asset. (a) The underlying asset’s payoff is always S T , whereas the put’s payoff is 0 if S T ≥ 22 . 5, and 22 . 5 S T if S T < 22 . 5. The payoff from the combined position is, by adding up the payoffs from the two assets, equal to S T +0 = S T if S T ≥ 22 . 5, and S T +22 . 5 S T = 22 . 5 if S T < 22 . 5. (b) The underlying asset’s payoff is always S T , whereas the call’s payoff is 0 if S T ≤ 22 . 5, and S T 22 . 5 if S T > 22 . 5. Since the strategy calls for writing a call, the payoff’s from the option position are 0 if S T ≤ 22 . 5, and ( S T 22 . 5) if S T > 22 . 5. The payoff from the combined position is, by adding up the payoffs from the two assets, equal to S T 0 = S T if S T ≤ 22 . 5, and S T ( S T 22 . 5) = 22 . 5 if S T > 22 . 5. (c) The payoff from the long call is 0 if S T ≤ 20, and S T 20 if S T > 20. The payoff from the written call is 0 if S T ≤ 25, and ( S T 25) if S T > 25. The payoffs from the portfolio are therefore 0 if S T ≤ 20; S T 20 if 25 > S T > 20; and S T 20 ( S T 25) = 5 if S T > 25. (d) The payoff from the long put is 0 if S T ≥ 25, and 25 S T if S T < 25. The payoff from the written put is 0 if S T ≥ 20, and (20 S T ) if S T < 20. The payoffs from the portfolio are therefore 0 if S T ≥ 25; 25 S T if 25 > S T > 20; and 25 S T (20 S T ) = 5 if S T < 20. (e) The payoff from the long put is 0 if S T ≥ 20, and 20 S T if S T < 20. The payoff from the long call is 0 if S T < 25, and S T 25 if S T > 25. The payoffs from the portfolio are therefore S T 25 if S T ≥ 25; 0 if 25 > S T > 20; and 20 S T if S T < 20. (f) If S T < 20, all call are outofthemoney and the payoff from the strategy is 0. If 20 < S T < 22 . 5, only the call with K = 20 will be inthemoney, and the payoff from the strategy is S T 20. If 22 . 5 < S T < 25, both the call with K = 20 and the call with K = 22 . 5 will be inthemoney: the payoff from the strategy is S T 20 2( S T 22 . 5) = 25 S T (note how each written call has a payoff of ( S T 22 . 5)). Finally, if S T > 25, then all calls are inthemoney, and the net payoff from the strategy is...
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.
 Fall '10
 Staff
 Derivatives, Options

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