Hi

Could anybody tell how to solve b and c?

Thank you!

nn 2016_07_27_Paper_Main_FM225_DRAFT.pdf Page 3 of 3 @ o 2 0, o Search 3. Risk Neutral Trees. (30 points) Assume that after you estimate the risk neutral model for the continuously compounded rate rij you arrive at the following tree: 0 1 2 t i 0 1 2 j 0 3% 6% 9% 1 2% 4% 1% There is an equal probability of moving up or down on the tree. The time period is one year (A = 1). (a) (5 marks] What advantage does the Black-Derman-Toy model have over the Ho-Lee model, when comparing the plausibility of the modeled interest rates? (b) (10 marks) Assume that you have zero coupon bond prices as well as cap prices available for any desired maturity. Briefly describe how you would proceed to fit the full Black-Derman-Toy model. Outline all the relevant steps. Explain why- once you have fitted the model-you cannot use the resulting tree to price zero coupon bonds or caps. () [15 marks] Price a 3-year coupon bond that pays an annual coupon of 5% only if the one year interest rate (annually compounded) at the beginning of the period is below 5%. Compare the resulting price to the price of a plain vanilla 3-year coupon bond that pays 5% annually. nn 2016_07_27_Paper_Main_FM225_DRAFT.pdf Page 3 of 3 @ o 2 0, o Search 3. Risk Neutral Trees. (30 points) Assume that after you estimate the risk neutral model for the continuously compounded rate rij you arrive at the following tree: 0 1 2 t i 0 1 2 j 0 3% 6% 9% 1 2% 4% 1% There is an equal probability of moving up or down on the tree. The time period is one year (A = 1). (a) (5 marks] What advantage does the Black-Derman-Toy model have over the Ho-Lee model, when comparing the plausibility of the modeled interest rates? (b) (10 marks) Assume that you have zero coupon bond prices as well as cap prices available for any desired maturity. Briefly describe how you would proceed to fit the full Black-Derman-Toy model. Outline all the relevant steps. Explain why- once you have fitted the model-you cannot use the resulting tree to price zero coupon bonds or caps. () [15 marks] Price a 3-year coupon bond that pays an annual coupon of 5% only if the one year interest rate (annually compounded) at the beginning of the period is below 5%. Compare the resulting price to the price of a plain vanilla 3-year coupon bond that pays 5% annually