Kevin Swinson is the finance director of Mountainbrook Trading plc. The board of directors has just granted Mr Swinson 30,000 at-the-money European call options on the company’s equity, which is currently trading at £30 per share.
The equity pays no dividends. The options will expire in 4 years, and the standard deviation of the returns on the shares is 55 per cent. Treasury bills that mature in 4 years currently yield a continuously compounded interest rate of 3 per cent.

(a) Use the Black–Scholes model to calculate the value of the share options.

(b) You are Mr Swinson’s financial adviser. He must choose between the previously mentioned share option package and an immediate £500,000 bonus. If he is risk-neutral, which would you recommend?

(c) How would your answer to

(b) change if Mr Swinson were risk-loving and he could not sell the options prior to expiration?