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A stock currently trades at £20. The market homogeneously agrees that in one year the stock price will either go up by 50% or fall by 30%. The one-period risk-free rate at which investors can borrow and lend is 5% per year. A European call option on this stock that expires in one year has an exercise price of £22.
(i) Use the single period binomial option pricing model to find the arbitrage-free price of the call option today.
(ii) Suppose that as opposed to your calculation in part (i), the European call option on the same stock with the same maturity and exercise price is trading at £4.00 in the market. Are there any arbitrage opportunities? If yes, demonstrate how one can profit from this possibility (Hint: Use the replicating portfolio that guarantees a riskless payoff to the seller of the call option).
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