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# ps8 - ECO 362 PROBLEM SET 81 FINANCIAL INVESTMENTS...

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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 and with the 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 , we have to: 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 fi 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 ff \$100 at maturity in one year. The principal and interest on the \$95 it costs to buy this synthetic bond would be \$94 × 1 . 04 = \$98 . 8 . Thus, there would be a pure arbitrage pro fi

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