Q4. This question concerns the following binomial model for the 1-year LIBOR rate. The current rate...
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Q4. This question concerns the following binomial model for the 1-year LIBOR rate. The current rate is r(0, 1) = r = 0.0500; in one year, the rate can be r = 0.0600 or rd = 0.0400. Finally, the current 2-year rate is r(0, 2) = 0.0510. (All rates are with annual compounding.) a) Consider a European put with maturity T on a zero-coupon bond that matures at T' = 2 with a strike of Kp = 95 per 100 face. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as this put at time T = 1? b) What is the price of the put? c) Consider a caplet maturing at T' = 2 that pays to the owner, on date T', interest at rate r(T' - 1,7") net of the fixed rate Kc = 0.0520, if the owner elects to receive the payment. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as the value of this caplet at time T = 1 on a notional amount N = $10,000? d) What is the value of this contract (on the notional amount N = $10,000)? e) Compute the risk-neutral probabilities consistent with the given tree and zcb prices. f) What are the possible values of the return between 0 and 1 on the zcb maturing at 2, and what is the expectation of this return under the risk-neutral probability (i.e., the weighted average of the returns using the RNP as weights)? Answer the same questions for the return between 0 and 1 of the put, and compare with the bond. How would you describe the comparison? g) Verify the answers to parts b) and d) using the risk-neutral probabilities. Q4. This question concerns the following binomial model for the 1-year LIBOR rate. The current rate is r(0, 1) = r = 0.0500; in one year, the rate can be r = 0.0600 or rd = 0.0400. Finally, the current 2-year rate is r(0, 2) = 0.0510. (All rates are with annual compounding.) a) Consider a European put with maturity T on a zero-coupon bond that matures at T' = 2 with a strike of Kp = 95 per 100 face. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as this put at time T = 1? b) What is the price of the put? c) Consider a caplet maturing at T' = 2 that pays to the owner, on date T', interest at rate r(T' - 1,7") net of the fixed rate Kc = 0.0520, if the owner elects to receive the payment. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as the value of this caplet at time T = 1 on a notional amount N = $10,000? d) What is the value of this contract (on the notional amount N = $10,000)? e) Compute the risk-neutral probabilities consistent with the given tree and zcb prices. f) What are the possible values of the return between 0 and 1 on the zcb maturing at 2, and what is the expectation of this return under the risk-neutral probability (i.e., the weighted average of the returns using the RNP as weights)? Answer the same questions for the return between 0 and 1 of the put, and compare with the bond. How would you describe the comparison? g) Verify the answers to parts b) and d) using the risk-neutral probabilities.
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a To replicate the payoff of the European put at time T 1 we need to find the portfolio of the 1year and 2year zerocoupon bonds that has the same payoff Lets denote the price of the 1year zerocoupon b... View the full answer
Related Book For
Financial accounting
ISBN: 978-0136108863
8th Edition
Authors: Walter T. Harrison, Charles T. Horngren, William Bill Thomas
Posted Date:
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