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An investor has decided to model PPB ple shares using the lognomal model. Using historical data, she has estimated the drift and volatility parameters to be 6% and 25% respectively. PPB's current share price is $2. Calculate the mean and variance of PPD's chare price in one year's time. [3] Calculate the probability that. (a) PPB's shares fall in value over the neal year. (b) PPB's shares yield aretum of greater than 30% over the next year. Assume that no dividends are to be paid over the next year. (41 [Total 7]Company X issues 3-month European call options on its own shares with a strike price of 120p. They are currently priced at 30 pence per share. The current share price is 123p and the current force of interest is 6 = 6%% pa. If dividends are payable continuously at a rate of q = 12% pa then calculate the fir price for put options on the share price at the same strike price. Explain the strategy for arbitrage profit if, instead, the price of the put options is 25p.State what is meant by put-call parity. 121 (ii) By constructing two portfolios with identical payoffs at the exercise date of the options, derive an expression for the put-call parity of a European option on a share that has a dividend payable prior to the exercise date. [6] (iin) If the equality in (ii) does not hold, explain how an arbitrageur can make a riskless profit. (3] [Total 1 1]