Experts required here

1 The Black-Scholes model for stock prices The Black-Scholes model describes the price of stock at time : as a stochastic process {S, : ( 2 0}, determined by S, = Soexp(ut + 5X,). where So is the initial price of the stock, {X : f 2 0) is a standard Wiener process, and the constants & and o > 0 are the drift rate and the volatility, respectively. A European call option on the stock with strike price c and expiry time fo is a contract that gives the buyer the right (but not the obligation) to buy one unit of the stock at time fo at price c. The buyer will only exercise this option if So, > c, in which case the payoff is given by C= (Sto -c)+ = max{Sto - c. 0). The classical Black-Scholes formula establishes the price at time 0 of this European call option as Pho = E [e -to C] = E lepto (Sto - c)+], where p is the interest rate, and under the assumption that a = p -g/2. Note that this choice of it is the one that means the expected discounted stock price is constant. This formula can be written as P. = 50 (108(So/c) + (p+ a /2)to ) - re-prog ( los(So/c) + (p - G /2)to avto Plot {A :0