Timet Period i 0 0 -3.83044 0.1877 0.25 1 -3.61935 0.1866 0.50 2 -3.43890 0.2776 0.75 3 -3.15590 27,0 O i Suppose that you estimated the following parameters for the full Black, Derman and Toy model (1990): (a) [25 marks] Based on the model parameters, construct the risk-neutral tree of interest rates. (b) [25 marks] Find the 1-year swap rate for a swap defined on the 3-month rate with quarterly payments. (C) [25 marks] Plot the fixed-for-floating swap value tree for the swap with the nominal value $100 and the swap rate that you found in (b). [Hint: recall that swap is determined with respect to the quarterly compounded rate.] (d) [25 marks] Consider a European payer swaption with 6 months to maturity (i = 2), to enter at i = 2 into a 6-month swap that you considered in (c) (i.e. the maturity of the swap is 1 year from now). Calculate the price of this swaption. = Timet Period i 0 0 -3.83044 0.1877 0.25 1 -3.61935 0.1866 0.50 2 -3.43890 0.2776 0.75 3 -3.15590 27,0 O i Suppose that you estimated the following parameters for the full Black, Derman and Toy model (1990): (a) [25 marks] Based on the model parameters, construct the risk-neutral tree of interest rates. (b) [25 marks] Find the 1-year swap rate for a swap defined on the 3-month rate with quarterly payments. (C) [25 marks] Plot the fixed-for-floating swap value tree for the swap with the nominal value $100 and the swap rate that you found in (b). [Hint: recall that swap is determined with respect to the quarterly compounded rate.] (d) [25 marks] Consider a European payer swaption with 6 months to maturity (i = 2), to enter at i = 2 into a 6-month swap that you considered in (c) (i.e. the maturity of the swap is 1 year from now). Calculate the price of this swaption. =