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1. For t T, let P(t, T, r) be the price at time t of a zero-coupon bond that pays $1 at time T, if

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1. For t T, let P(t, T, r) be the price at time t of a zero-coupon bond that pays $1 at time T, if the short-rate at time t is r. You are given: (i) P(t, T,r) = A(t, T)exp[-B(t, T)r] for some functions Alt, T) and B(t,T). (ii) B(0, 3) = 2. Based on P(0, 3, 0.05), you use the delta-gamma approximation to estimate P(0, 3, 0.03), and denote the value as Pest(0,3, 0.03) Find Pest(0,3, 0.03) P(0,3, 0.05) 2. Several months ago, an investor sold 100 units of a one-year European call option on a nondividend- paying stock. She immediately delta-hedged the commitment with shares of the stock, but has not ever re-balanced her portfolio. She now decides to close out all positions. You are given the following information: (i) The risk-free interest rate is constant. (ii) The stock price changes from 40 usd to 50 usd. The call price changes from 8.88 usd to 14.42 usd. Put option price changes from 1.63 usd to 0.26 usd. Denote that the delta of the call option is 0.794. The put option above is a European option on the same stock and with the same strike price and expiration date as the call option. Calculate her profit. 1. For t T, let P(t, T, r) be the price at time t of a zero-coupon bond that pays $1 at time T, if the short-rate at time t is r. You are given: (i) P(t, T,r) = A(t, T)exp[-B(t, T)r] for some functions Alt, T) and B(t,T). (ii) B(0, 3) = 2. Based on P(0, 3, 0.05), you use the delta-gamma approximation to estimate P(0, 3, 0.03), and denote the value as Pest(0,3, 0.03) Find Pest(0,3, 0.03) P(0,3, 0.05) 2. Several months ago, an investor sold 100 units of a one-year European call option on a nondividend- paying stock. She immediately delta-hedged the commitment with shares of the stock, but has not ever re-balanced her portfolio. She now decides to close out all positions. You are given the following information: (i) The risk-free interest rate is constant. (ii) The stock price changes from 40 usd to 50 usd. The call price changes from 8.88 usd to 14.42 usd. Put option price changes from 1.63 usd to 0.26 usd. Denote that the delta of the call option is 0.794. The put option above is a European option on the same stock and with the same strike price and expiration date as the call option. Calculate her profit

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