Financial Derivatives and Financial Engineering Formative Test 2023/24

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Financial Derivatives and Financial Engineering Formative Test 2023/24

24-hour open book test. Maximum words, 1,500

Answer any one of the following questions 

1. The current market share price of Rafferty plc is £25. Every month, the stock price is expected either to increase by a multiplicative factor u = 1.1, or decrease by a multiplicative factor d. The annual continuously compounded risk-free rate of interest in the economy is 4.5%.

(a) What, according to the binomial option pricing model, will be the price of a 3-month at-the-money European put option on a share of Rafferty stock? (25 marks)

(b) What will the price of the put option be if it is American style? (25 marks) 

(c) Rafferty plc is a constituent of the BROCK100 stock index which is currently trading at 5,000 index points and pays a continuously compounded dividend yield of 3%. Use the Black-Scholes model to calculate the price of a 6-month European-style index call option written on the BROCK100 with a contract multiplier of £10 per full index point.    (50 marks)

In each of parts (a), (b) and (c) you should explain and interpret your answer.

2. Koenan plc has a position in a stock portfolio comprising the companies listed in Table 1. Correlation coefficients between stock returns is given in the correlation matrix.

Table 1

Correlation Matrix

(a) Calculate the 10-day 97.5 percent value at risk (VaR) for the portfolio. (25 marks)

(b) Calculate the 10-day 97.5 percent VaR for equivalent positions in the individual assets. Identify and analyse any gains from diversification. (25 marks)

(c) Critically evaluate the model you have used in your analysis. (50 marks)

3. Guivarch Bank holds a €15m equity portfolio with a beta of 1.1 relative to the HEARD100 stock index. The HEARD100 is currently trading at 10,000 points and offers a continuously compounded dividend yield of 3%. The HEARD100 futures contract has a contract multiplier of €10 per full index point and matures in 6 months. The current risk-free rate of interest is 5%.

(a) Calculate the futures position required to hedge the portfolio using a beta hedge. (25 marks) 

(b) Three months later the HEARD100 has fallen 10% to 9,000. Calculate the new futures price and the gain or loss on the futures and spot positions. (25 marks) 

(c) Explain and critically evaluate this hedging strategy and discuss important issues in hedging with stock index futures. (50 marks)