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Consider a three-period binomial tree model for a stock price process $, , under which the stock price either rises by 18% or falls by 15% each month. No dividends are payable. The continuously compounded risk-free rate is 0.25% per month. Let So =$85. Consider a European put option on this stock, with maturity in three months (i.e. at time / = 3) and strike price $90. (i) Calculate the price of this put option at time ? = 0. [4] (ii) Calculate the risk-neutral probability that the put option expires out-of-the- money. [2] (Hii) Assess whether the probability calculated in part (ii) would be higher or lower under the real-world probability measure. [No further calculation is required.] [3] [Total 9] The market price ", of a traded security satisfies the following stochastic differential equation dS, =(1-20)5,di +65,dw. where I, is a standard Brownian motion under the probability measure p* . (i) Determine the value of 2 such that the discounted asset price process 5, =e-"S, is a martingale under the given probability measure [3] (ii) Explain whether the probability measure P"is the real-world or risk-neutral measure, for the value of 2 obtained in part (i) [3] [Total 6]