Please help to answer the following questions:

6. (23 points) The prices ofzeroccupon bonds (each with a face value of$100) are given in the table on the right. (4 points) Fit the simple Black-Herman-Toy m model to the zero-coupon bond prices. The length of a time period in the model shall be A = 0.25 \"93.51 years, and the volatility of the logarithm of the short rate is a = 10%. What are the 60,91, and 92 values? Your answer should consist of the three 6' values, and a short (max. four sentences) description of how you obtained them. {4 points) Based on the model which you tted in question a, calculate the price of a cap with maturity at t = 0.5 (i.e., the last cash ow ofwhich 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 ow payments