Solve question 5& 6.

The interest rate curve for a particular economy is flat, in such a way that all zero coupon interest rates i(() are equal to some constant i, for all f 2 0. An arbitrage free environment can be assumed, and transaction costs, taxes and payment conventions can be ignored. Derive the fixed payment c on a standard five-year annual par swap, one which pays an annual fixed amount against an annual floating amount, set at the beginning of each period and paid in arrears. [3] Show that the fixed payment cy payable twice per year on a five-year semi- annual par swap, otherwise on the same basis as in (1), is not [1] (iii) Derive the fixed payment cy on a five-year annual par swap similar to that in (i) above, but for which the annual floating payment is set in arrears on the payment date itself. (This is known as a LIBOR-in-Arrears swap.) (3] (iv) Derive the fixed payment ca on a five-year annual par swap similar to that in (i) above, but for which the annual floating payment, set at the beginning of the period and paid in arrears, is calculated to be the level of the five year par swap as calculated in (i) above. (This is known as a Constant Maturity Index swap.) (3] (v) If the zero coupon interest curve is upwards sloping, i.c. i(t,) > i(f,) for all 12 2 1. describe how the answer in sections (ili) and (iv) above will be affected. (2] [Total 12] 6 A fund manager has a well diversified portfolio that tracks the performance of the 5&P 500 and is worth $275m. The current value of the S&P 500 is 1,100. The manager would like to buy portfolio insurance against a reduction of more than 5% in the value of the portfolio over the next year. The risk free rate is 5% p.a. The dividend yield on both the portfolio and the S&P 500 is 3%. The market implied volatility for the S&P 500 is currently 25% p.a. (1) Calculate the cost of hedging the portfolio using European put options. [4] Describe alternative strategies involving European call options which would have the same effect as the options in (i). (3] Calculate the initial (delta) position if the manager sought to replicate the effect of the put options by investing part of the portfolio in risk-free securities. [21 (iv) Calculate the initial number of futures contracts required if, instead of risk-free securities in (ili), the manager decided to use 9-month index futures contracts, cach contract nominal being 250 times the index. (31