A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, the financial institution pays fixed rate of 4% per annum and receives 12 month LIBOR (with 30/360 day basis) on a principal of $10 million every year for six years. Interest rate (with annual compounding) moved up to 5% per annum for all maturities after six months and stayed there since then. Suppose further that the credit quality of company X started to deteriorate two years after and then defaulted right before it made the third payment (at the end of year 3).

a. What is the value of the swap to the financial institution then (i.e. at the end of year 3)? Please draw the cashflow diagram when illustrating your answers.

b. What is the loss to the financial institution, if any, assuming the recovery ratio is 30%?

c. Company X entered into the swap three years ago in order to hedge the interest payments of a bond it issued back then. In your opinion, what is likely to be the historical movement of the price of the bond in the past three years? Please explain in details.