a Assume that a stock S that pays no dividends undergoes geometric Brownian motion with an expected return u and a volatility o. Imagine a derivative log contract L(S,t) that pays off InS(T) in US dollars at time T, where S(T) is the value of the stock price at time T. a (a) From Ito you know the stochastic process for InS(t). Calculate the value of the security L(S(t), t) in terms of the stock price S(t) at time t by using our knowledge that the value of a derivative is the expected riskless discounted value of the terminal payoff in the risk-neutral q- [15 points] (b) Show that the solution for L(S(t), t) satisfies the Black-Scholes PDE.[ [15 points] measure. a Assume that a stock S that pays no dividends undergoes geometric Brownian motion with an expected return u and a volatility o. Imagine a derivative log contract L(S,t) that pays off InS(T) in US dollars at time T, where S(T) is the value of the stock price at time T. a (a) From Ito you know the stochastic process for InS(t). Calculate the value of the security L(S(t), t) in terms of the stock price S(t) at time t by using our knowledge that the value of a derivative is the expected riskless discounted value of the terminal payoff in the risk-neutral q- [15 points] (b) Show that the solution for L(S(t), t) satisfies the Black-Scholes PDE.[ [15 points] measure