Homework 10. Consider the Black-Scholes model for a stock price (St), dSt = u Stdt + o StdBt, So = 1, where (Bt) is a Brownian motion under P. In addition, let B4 = ert be the value of the savings account. Let B+ = Bt + 4-2rt. (a) Explain why there exists a probability measure equivalent to P such that (Bt) is a Brownian motion under O. (b) Show through calculation that (St/Bt) is not a martingale under . You may use that the solution to the Black-Scholes SDE is S = e(k={o?)t+oB!! Hint. The exponential martingale of Brownian motion may help you here! (c) The Black-Scholes model is complete and possesses the EMM Q which turns B= B+ + u-r t o into a Brownian motion. By solely appealing to completeness of the model, explain why (St/Bt) could never have been a martingale under Q. Homework 10. Consider the Black-Scholes model for a stock price (St), dSt = u Stdt + o StdBt, So = 1, where (Bt) is a Brownian motion under P. In addition, let B4 = ert be the value of the savings account. Let B+ = Bt + 4-2rt. (a) Explain why there exists a probability measure equivalent to P such that (Bt) is a Brownian motion under O. (b) Show through calculation that (St/Bt) is not a martingale under . You may use that the solution to the Black-Scholes SDE is S = e(k={o?)t+oB!! Hint. The exponential martingale of Brownian motion may help you here! (c) The Black-Scholes model is complete and possesses the EMM Q which turns B= B+ + u-r t o into a Brownian motion. By solely appealing to completeness of the model, explain why (St/Bt) could never have been a martingale under