Analyze a two-year swap agreement to exchange LIBOR for fixed-rate payments on a $100 million notional principal. The first payment will be made in one year; the second in two years. You have the following information on LIBOR rates: One-year spot rate is 3% per year. Forward rate in the second year is 5% per year. What must be the annualized two-year spot LIBOR rate? Find the floating-rate payments to be made. Find the present value of the floating-rate payments. Find the fixed rate that would price the swap correctly. Now suppose that at T=1, just after the first payments were made, interest rate over year two turns out to be 6% per year (instead of 5% originally estimated). Which party is at a loss now: the one making the fixed payments, or the one making the floating payments? Which party faces credit risk? Initials: 12 of 13 B) As a black hole radiates at temperature TBH, it must lose mass in order to conserve energy. Use the relation Q = TdS to derive a formula for the amount of heat radiated when the black hole loses an amount of mass dM. C) Integrate your formula from (B) to evaluate the total amount of heat radiated mass of our black hole decreases from M to 0. Use this to argue that the work d black hole as it evaporates is zero. This question is on solutions of the Black-Scholes equation. The Black-Scholes formula for the value of a put option P (S,t) on a non-dividend paying stock, is P(S,t) = -SN(-d) + Ee-(T-t) N(-d) From this expression, find the Black-Scholes value of the put option in the following limits: a. (time tends to expiry) tT, > 0; b. (volatility tends to zero) 0, t