Part A

1.  A portfolio manager has a €500m position in an equity portfolio which tracks the WSM250  index. The manager is concerned about the possibility of a short term fall in the index and   consequent decrease in the value of his portfolio. To address this issue the fund manager   decides to hedge using futures written on the WSM250 index. The current value of the        index is 3,000 points with a continuously compounded dividend yield of 2. 1%. The portfolio has a beta of 1.15 with respect to the index. The relevant futures contract has 10 months to maturity and has a contract multiple of €20 per full index point. The risk-free rate of interest is 2.75%.

(a) Calculate the futures position required to hedge the portfolio using a beta hedge and

explain each step in the process.                                                                 (30 marks)

(b) After 4 months the spot price of the index falls to 2,850 points and the futures position is closed out. Calculate the new quoted futures price, the gain or loss on the futures and   spot positions and return on the hedged portfolio. Explain your findings.    (40 marks)

(c) Discuss whether this is likely to be a perfect hedge.                                    (30 marks)

2.  An interest rate swap with notional value of £100m has a remaining life of 9 months. The terms of the swap require the 6-month LIBOR to be exchanged for 5.5% per annum with semi-annual compounding. The current swap rate being exchanged for LIBOR in swaps of all maturities is 4.75% per annum with continuous compounding. Three months ago the 6- month LIBOR was 5.25% per annum.

(a) Explain, using a diagram, how the swap is constructed.                              (30 marks)

(b) Calculate the value of the swap to the party paying the floating rate. Assume that the

swap takes place without involving a financial intermediary.

(c) Discuss the principle that underpins swap valuation.

(40 marks)

(30 marks)

3.   Shares of Scruggs Inc. are currently trading at $27 with volatility of returns of 22% per annum. The annual continuously compounded risk-free rate of interest is 2%.

(a)  Use the Black Scholes option pricing model to price a 3-month European-style put

option written on Scruggs Inc. with an exercise price of $30 and interpret your findings. (30 marks)

(b)  Every month, the share price is expected either to increase, by a multiplicative factor of

u = 1.1, or decrease. Construct a binomial tree to price the option if it is American-style, discuss the process and interpret your findings.

(30 marks)

(c)  Scruggs Inc. features in the FLATT500 stock index, which pays a continuous dividend  yield of 1.2%, has a contract multiplier of $100 per full index point and volatility of         returns of 20% per annum. Calculate the price of a five-month at-the-money European- style call option when the index is at 2,500 points and interpret your findings.

(40 marks)

Part B

4. Present and critically evaluate the bond price and contingent claims approaches to the estimation of default probabilities.

5. Critically evaluate the historical simulation and model building approaches to value at risk.

6. Derive the Black Scholes (1973) model and critically analyse the Black Scholes Merton approach to option pricing.

7. Discuss the range of securities available in derivative markets designed with the purpose of managing energy, weather and insurance risks, and explain and analyse the growth in        demand for these securities.