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1. (4 points) Using a no-arbitrage argument, show that (a) ( point) Ca 2 max0, So -K. (b) (I point) So 2 CA (c) (

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1. (4 points) Using a no-arbitrage argument, show that (a) ( point) Ca 2 max0, So -K. (b) (I point) So 2 CA (c) ( point) PA 2 max(0, K - Sol (d) point) PA S K 2. (4 points) Consider an American Put on a non-dividend-paying stock, show that PA 2 max(0, KeT - Sol. 3. (4 points Suppose we are dealing with a stock that does not pay any dividends. (a) (2 points) We own an American Call on this stock, and So > K, and we price will go below K, should have strong reason to believe that the stock we exercise the American Call? Give me your reasons. (b) (2 points) We own an American Put on this stock, and So CA - PA, and (b) (2 points) CA PA> So -KeT. 6. (4 points) Let us consider the case of American Calls on a dividend-paying stock for this problem. Let us suppose the expected dividend date is te. and 00, it is never optimal to exercise the American Call before the expected dividend date; or, after the expected dividend date, but before expiration. That is, if we were to exercise the American Call before expiration, it can only be either "just-before-t," (ie. ) or "just-after-4 (i.e. It). 1. (4 points) Using a no-arbitrage argument, show that (a) ( point) Ca 2 max0, So -K. (b) (I point) So 2 CA (c) ( point) PA 2 max(0, K - Sol (d) point) PA S K 2. (4 points) Consider an American Put on a non-dividend-paying stock, show that PA 2 max(0, KeT - Sol. 3. (4 points Suppose we are dealing with a stock that does not pay any dividends. (a) (2 points) We own an American Call on this stock, and So > K, and we price will go below K, should have strong reason to believe that the stock we exercise the American Call? Give me your reasons. (b) (2 points) We own an American Put on this stock, and So CA - PA, and (b) (2 points) CA PA> So -KeT. 6. (4 points) Let us consider the case of American Calls on a dividend-paying stock for this problem. Let us suppose the expected dividend date is te. and 00, it is never optimal to exercise the American Call before the expected dividend date; or, after the expected dividend date, but before expiration. That is, if we were to exercise the American Call before expiration, it can only be either "just-before-t," (ie. ) or "just-after-4 (i.e. It)

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