Assume that you have the rights to a coal mine and the most recent valuation of the mine was £6.6 million. Because of increasing demand from Asia, the price of similar mines has grown by 15 per cent per annum, with an annual standard deviation of 25 per cent. A buyer has recently approached you and wants an option to buy the mine in the next 12 months for £6.9 million. The risk-free rate of interest is 5 per cent per year, compounded continuously.
Required:
How much should you charge for the option?