i=0 i=1 i=2 T2, 0.1299 T1,u=0.0868 To=0.04 12.ud 0.0723 T1,d=0.0268 12,dd = 0.0147 You have estimated...

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i=0 i=1 i=2 T2, 0.1299 T1,u=0.0868 To=0.04 12.ud 0.0723 T1,d=0.0268 12,dd = 0.0147 You have estimated the risk neutral interest rate tree for the continuously compounded interest rate as in the table above. There is equal risk neutral probability to move up or down the tree and each interval time represents 6 months, that is, = 0.5. Part I: 1. Compute the discount factors for all maturities. = 2 if the continuously 2. Compute the price of a security that pays $100 at time i compounded interest rate at that time is more than 7.00% and zero otherwise. 3. Compute the price of a 1.5-year cap, with semi-annual payment, strike rate r = 5%, and notional N : 100. Part II: = Answer the questions of Part I using the Monte-Carlo Simulations approach. You have to precisely explain your reasoning and to show the standard error, as well as the confidence interval. Compare the results obtained in both parts. i=0 i=1 i=2 T2, 0.1299 T1,u=0.0868 To=0.04 12.ud 0.0723 T1,d=0.0268 12,dd = 0.0147 You have estimated the risk neutral interest rate tree for the continuously compounded interest rate as in the table above. There is equal risk neutral probability to move up or down the tree and each interval time represents 6 months, that is, = 0.5. Part I: 1. Compute the discount factors for all maturities. = 2 if the continuously 2. Compute the price of a security that pays $100 at time i compounded interest rate at that time is more than 7.00% and zero otherwise. 3. Compute the price of a 1.5-year cap, with semi-annual payment, strike rate r = 5%, and notional N : 100. Part II: = Answer the questions of Part I using the Monte-Carlo Simulations approach. You have to precisely explain your reasoning and to show the standard error, as well as the confidence interval. Compare the results obtained in both parts.