1. A variable x follows the stochastic process in which a and b are constants and is a Wiener process. Consider variable.
2. Using Ito's lemma, derive the process for.

1. In the Black-Scholes-Merton model, what variables do x and y correspond to?

1. On October 12, the S&P 500 index (SPX) was trading at 3,477.13. The price of a European put option on the index expiring on December 4 with strike of 3300 is 71.67. Assuming the risk-free interest rate for the period from October 12 to December 4 is 0% p.a, the annual dividend rate on the SPX is 1.75%, and there are 40 trading days over that period (i.e. T=40/252), compute the implied volatility for the option.