(Swap a fixed rate vs. a short rate) Consider the following version of an interest rate swap. The contract is made between two parties, A and B, and the payments are made as follows:
• A (hypothetically) invests the principal amount K at time 0 and lets it grow at a fixed rate of interest R (to be determined below) over the time interval [0, T ].
• At time T the principal will have grown to KA SEK. A will then subtract the principal amount and pay the surplus K − KA to B (at time T ).
• B (hypothetically) invests the principal at the stochastic short rate of inter- est over the interval [0, T ].
• At time T the principal will have grown to KB SEK. B will then subtract the principal amount and pay the surplus K − KB to A (at time T ).
The swap rate for this contract is now defined as the value, R, of the fixed rate which gives this contract the value zero at t = 0. Your task is to compute the swap rate.