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Unformatted text preview: Derivative Securities, Fall 2007 – Homework 3. Distributed 10/3/07, due 10/17/07. Typo in problem 3 corrected: a squared call has payoff ( F T- K ) 2 + . A solution sheet to HW2 will be posted 10/11; a solution sheet to HW3 will be posted 10/25; no late HW’s will be accepted once the corresponding solution sheet has been posted. Problem 1 provides practice with lognormal statistics. Problems 2-5 explore the conse- quences of our formula for the value of an option as the discounted risk-neutral expected payoff. Problem 6 makes sure you have access to a numerical tool for playing with the Black-Scholes formula and the associated “Greeks.” Problem 7 reinforces the notion of “implied volatility.” Convention: when we say a forward price F t is “lognormal with drift μ and volatility σ ” we mean ln F t- ln F s is Gaussian with mean μ ( t- s ) and variance σ 2 ( t- s ) for all s < t ; here μ and σ are constant. In this problem set we will consider only options on a forward price, and we always assume that the forward price is lognormal. 1. Consider a forward price that’s lognormal with drift μ and volatility σ . Suppose the forward price now is F ....
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- Fall '11