6. (23 points) The prices of zero-coupon bonds (each with a Maturity (years) Price (dollars) face value of $100) are given in the table on the right. 0.25 98.43 a. (4 points) Fit the simple Black-Derman-Toy 0.50 96.81 model to the zero-coupon bond prices. The length 0.75 95.16 of a time period in the model shall be A = 0.25 1.00 93.51 years, and the volatility of the logarithm of the short rate is o = 10%. What are the 60,01, and 0, values? Your answer should consist of the three & values, and a short (max. four sentences) description of how you obtained them. b. (4 points) Based on the model which you fitted in question a., calculate the price of a cap with maturity at t = 0.5 (i.e., the last cash flow of which is at t = 0.5), which has a face value of $100, a strike rate of 5.5% (with quarterly compounding), and which has quarterly cash flow payments. 6. (23 points) The prices of zero-coupon bonds (each with a Maturity (years) Price (dollars) face value of $100) are given in the table on the right. 0.25 98.43 a. (4 points) Fit the simple Black-Derman-Toy 0.50 96.81 model to the zero-coupon bond prices. The length 0.75 95.16 of a time period in the model shall be A = 0.25 1.00 93.51 years, and the volatility of the logarithm of the short rate is o = 10%. What are the 60,01, and 0, values? Your answer should consist of the three & values, and a short (max. four sentences) description of how you obtained them. b. (4 points) Based on the model which you fitted in question a., calculate the price of a cap with maturity at t = 0.5 (i.e., the last cash flow of which is at t = 0.5), which has a face value of $100, a strike rate of 5.5% (with quarterly compounding), and which has quarterly cash flow payments