The swap rate for this contract is defined as the value R of the fixed rate which gives this contract the value zero at t=0. Compute the swap rate.

Exercise 5.7 Swap a fixed rate vs. a short rate. Consider the following version of an interest rate swap contract between two parties A and B. The payments are as follows: A hypothetically invests the principal amount K at time t = 0 and lets it grow at fixed continuously compounded rate of interest R (to be determined below) over the time interval [0, T]. At T the principal will have grown to KA. A will then pay the surplus KA - K to B. B hypothetically invests the principal amount K at the stochastic short rate of interest r(t) over the interval [0, T]. At T the principal will have grown to KB. B will then pay the surplus KB - K to A. Exercise 5.7 Swap a fixed rate vs. a short rate. Consider the following version of an interest rate swap contract between two parties A and B. The payments are as follows: A hypothetically invests the principal amount K at time t = 0 and lets it grow at fixed continuously compounded rate of interest R (to be determined below) over the time interval [0, T]. At T the principal will have grown to KA. A will then pay the surplus KA - K to B. B hypothetically invests the principal amount K at the stochastic short rate of interest r(t) over the interval [0, T]. At T the principal will have grown to KB. B will then pay the surplus KB - K to A