Question 1 (a) In the context of the one-period BOPM, what is a risk-neutral probability? Show that this risk-neutral probability is consistent with the assumption that the underlying asset S grows at the risk-free rate. (b) What is implied volatility? How can it be calculated? (c) The current price of a forward contract for delivery of a non-dividend-paying stock in 3 months is $43 and the current stock price of stock is $40. Assuming that the 3-month risk free interest rate is 5% per annum, do you think there is an arbitrage opportunity? If so, explain briefly and how you would take advantage of it. (d) Suppose S follows a standard geometric Brownian motion (GBM) dS = (uS)dt +(S)dz. What is the process followed by In S? Question 1 (a) In the context of the one-period BOPM, what is a risk-neutral probability? Show that this risk-neutral probability is consistent with the assumption that the underlying asset S grows at the risk-free rate. (b) What is implied volatility? How can it be calculated? (c) The current price of a forward contract for delivery of a non-dividend-paying stock in 3 months is $43 and the current stock price of stock is $40. Assuming that the 3-month risk free interest rate is 5% per annum, do you think there is an arbitrage opportunity? If so, explain briefly and how you would take advantage of it. (d) Suppose S follows a standard geometric Brownian motion (GBM) dS = (uS)dt +(S)dz. What is the process followed by In S