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Unformatted text preview: 1 of 2 NBA 673 Introduction to Derivatives Homework 1 Problem 1 : Zero-Coupon Bond Price Maturity (Days) i d i s i c r .999182 30 .009952 .009960 .01 .009956 .996750 60 .019771 .019835 .02 .019803 .992738 90 .029451 .029667 .03 .029559 .980844 180 .038844 .039603 .04 .039221 The conventional length of the year has been set to 365 days in all computations above. We asked you to show your calculations. At a minimum, besides writing down the numerical values above, you should have indicated which formulas you are using. For all maturities, we have that i s > i d and i c > r. Problem 2 : (a) (b) S stock portfolio short call K K S cash portfolio short put stock K K S stock portfolio short call K K S stock portfolio short call K K S cash portfolio short put stock K K S cash portfolio short put stock K K Note that stock call = cash put (assuming the same strike price K for options). It is thus possible to have various portfolios of options, stock and cash holdings that have the same payoff. (c) The payoff of the trivial portfolio consisting of only one unit of stock dominates the payoffs of the two other portfolios. The portfolios we have created give up the upside their payoff is such that it follows the stock price on the interval [0, K], but then it stays constant at K for stock prices above the...
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- Spring '06