ps8 - ECO 362 December 13, 2007 PROBLEM SET 81 FINANCIAL...

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ECO 362 December 13, 2007 PROBLEM SET 8 1 FINANCIAL INVESTMENTS Professor: Burt Malkiel Exercise 1 (a) The Put-Call parity states C 0 = S 0 + P 0 μ 1 1+ r f T X where S 0 is the current price of the stock, C 0 and P 0 are the current value of European call and put options written on S andw iththe same strike (exercise price) X and same time to expiration T , and r f is the risk free rate. Hence, to replicate a one-year pure discount bond with a face value of $100 ,wehaveto : buy a share of stock, buy European put with an exercise price of $100 ,and sell a European call with an exercise price of $100 . (b) We know T =1 , X =100 S 0 = 100 , P 0 =10 ,and C 0 =15 . Then, the Put-Call parity formula X 1+ r f = S 0 + P 0 C 0 implies r f = X S 0 + P 0 C 0 1= 100 100 + 10 15 1=5 . 3% . (c) If r =4% , then one could make risk-free arbitrage pro f ts by borrowing at 4% and investing in synthetic one-year pure discount bonds consisting of a share of stock, a European put with exercise price $100 , and a short position in a European call with an exercise price $100 . The synthetic bond would cost $95 and pay o f $100 at maturity in one year. The principal and interest on the $95 it costs to buy this synthetic bond would be $94 × 1
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This note was uploaded on 10/15/2008 for the course ECO 362 taught by Professor Harrisonhong during the Fall '08 term at Princeton.

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ps8 - ECO 362 December 13, 2007 PROBLEM SET 81 FINANCIAL...

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