Question1

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An investor believes that each month the price of gold can either move up by 10% or down by 20%. (i) By using a risk-neutral valuation, calculate the price of a two-month at-the- money European style put option on gold (expressed as a percentage of the price of gold) if the risk-free rate of return is 2% per month and storage costs can be ignored. [4] (ii) An actuary calculates the same figure for the value of the option using a similar binomial gold price model. However, the actuary arrives at her figure by discounting the expected payoff from the option at a "risk discount rate". Assuming that the actuary's estimate of the probability of a 10% up-movement is 0.8, calculate the risk discount rate used by the actuary. [2] (iii) With reference to the riskiness (as defined in the capital asset pricing model) of investing in gold explain why the actuary's probability is plausible. [3] (iv) By considering the sign of the beta of this put option, explain how the risk discount rate used by the actuary can be justified. [2] [Total 11](i) One of the assumptions underlying the Black-Scholes model is that the price of the underlying follows a geometric Brownian motion. Explain briefly what this means and why this assumption may not be valid in practice. [4] (ii) State the other assumptions underlying the Black-Scholes model. [5] [Total 9]