The partners are still unhappy about one of the features of your analysis, namely your assumption that the coupon rate of the bond is equal to 6% per annum. Their thinking is that it is the coupon rate which should be adjusted in such a way that the initial value of the bond is equal to the desired amount.

(a) Assume that the face value of the bond issue is equal to one million dollars and that the coupon rate is given by C = 6%+S where S is a spread which is chosen in such a way that the initial value of the issue is equal to par. Should S be positive or negative?

(b) Determine the value of the spread S under the assumptions that the strike price and the volatility of the relevant forward swap rate are given by K = 1and

σ_swap(t) = 0:41(T - t)e^-0:65(T-t);

where T is the first fixing date of the underlying swap.