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The price of a non-dividend paying share, St, follows a geometric Brownian motion process. The current price of the share is £10 and volatility of the share price process is 12% per annum. The constant continuously compounded risk-free rate of interest is 4% per annum.
(a) Using Black-Scholes formula, show that the price of a European call option contract on the share with strike price £10 and 1 year to maturity is £0.69.
(b) Using put-call parity, or otherwise, calculate the price of a European put option contract on the share with strike price £10 and 1 year to maturity.
(c) Consider a strategy of simultaneously buying a 1-year European call option contract with strike price £10 and a 1-year European put option contract with strike price £10.
(i) Draw and label the consolidated pro t diagram for the strategy.
(ii) Outline the rationale behind the choice of this particular strategy.
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