No arbitrage pricing of options 1. Suppose you observe a binomial tree of 6-month risk-free spot rates

No arbitrage pricing of options

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1. Suppose you observe a binomial tree of 6-month risk-free spot rates and the spot rates shown below. A. Using true probability, what is the current price of a 12-month zero coupon bond at t if the bond has a face value of $800? (18pt) B. Using the annualized spot rate in the table, what is the current price of a 12-month zero coupon bond at to if the bond has a face value of $800? (4pt) C. What is the risk neutral probability PRN? (4pt) D. Assume that the bond is callable in six month with a call price of $784, what is the price of the call option at to? (6pt) E. Assume that the bond is puttable in six month with a put price of $784, what is the price of the put option at to? (6pt) Period 1 2 Years Annualized Spot Rate 0.5 4% 1.0 4.15% 3 1.5 4.25% to t t2 50% 5% 50% 4.5% 50% 4% 4% 50% 50% 3.5% 50% 3% 1. Suppose you observe a binomial tree of 6-month risk-free spot rates and the spot rates shown below. A. Using true probability, what is the current price of a 12-month zero coupon bond at t if the bond has a face value of $800? (18pt) B. Using the annualized spot rate in the table, what is the current price of a 12-month zero coupon bond at to if the bond has a face value of $800? (4pt) C. What is the risk neutral probability PRN? (4pt) D. Assume that the bond is callable in six month with a call price of $784, what is the price of the call option at to? (6pt) E. Assume that the bond is puttable in six month with a put price of $784, what is the price of the put option at to? (6pt) Period 1 2 Years Annualized Spot Rate 0.5 4% 1.0 4.15% 3 1.5 4.25% to t t2 50% 5% 50% 4.5% 50% 4% 4% 50% 50% 3.5% 50% 3%