3 The managers of Daylon plc are reviewing the company’s investment portfolio. About 15% of the port

问题

3 The managers of Daylon plc are reviewing the company’s investment portfolio. About 15% of the portfolio is represented by a holding of 5,550,000 ordinary shares of Mondglobe plc. The managers are concerned about the effect on portfolio value if the price of Mondglobe’s shares should fall, and are considering selling the shares. Daylon’s investment bank has suggested that the risk of Mondglobe’s shares falling by more than 5% from their current value could be protected against by buying an over the counter option. The investment bank is prepared to sell an appropriate six month option to Daylon for ￡250,000.

Other information:

(i) The current market price of Mondglobe’s ordinary shares is 360 pence.

(ii) The annual volatility (variance) of Mondglobe’s shares for the last year was 169%.

(iii) The risk free rate is 4% per year.

(iv) No dividend is expected to be paid by Mondglobe during the next six months.

Required:

(a) Evaluate whether or not the price at which the investment bank is willing to sell the option is a fair price.(10 marks)

参考答案

正确答案：

3 (a) The investment bank is offering to sell to Daylon plc an option to sell Mondglobe ordinary shares at a price no worse than 5% below the current market price of 360 pence. This is a put option on Mondglobe shares at a price of 342 pence. The Black-Scholes option pricing model may be used to estimate whether or not the option price is a fair price. The value of a put option may be found by first estimating the value of a call option and then using the put-call parity theorem.Basic data:Share price 360 penceExercise price 342 penceRisk free rate 4% (0·04)Volatility is measured by the standard deviation. The variance is 169% therefore the standard deviation, σ is 13% (0·13)The relevant period is six months (0·5)

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