Optional Exercise: Consider an European-style stock option which is issued at time i = 0 and matures at time 1 = T > 0. The option has no intermediate payoff and its final payoff at time T is given by or = (St - K)?, for a given strike K > 0. Suppose that the underlying stock price S follows a geometric Brownian motion with dynamics (this is the standard Black-Scholes-Merton framework) S = So +oS.W+bS. in which b,o e R are given parameters. The risk-free rate r > 0 is forever fixed, the underlying stock pays no dividends, and the market is complete. Calculate the price of this option at the time of issue (t = 0) as a function of the parameters in the model and the initial stock price So). Find a replicating trading strategy for this stock option. Optional Exercise: Consider an European-style stock option which is issued at time i = 0 and matures at time 1 = T > 0. The option has no intermediate payoff and its final payoff at time T is given by or = (St - K)?, for a given strike K > 0. Suppose that the underlying stock price S follows a geometric Brownian motion with dynamics (this is the standard Black-Scholes-Merton framework) S = So +oS.W+bS. in which b,o e R are given parameters. The risk-free rate r > 0 is forever fixed, the underlying stock pays no dividends, and the market is complete. Calculate the price of this option at the time of issue (t = 0) as a function of the parameters in the model and the initial stock price So). Find a replicating trading strategy for this stock option