3. Assume that a stock price is currently at $30. It is known that in one year stock price will be either $40 or $20. The annual interest rate is 5% with continuous compounding. Consider a European call option with strike price equal to $30 and 1 year to maturity and a European put option with strike price equal to $35 and 1 year to maturity. (1) What is the probability measure associated with stock being the numeraire? (2) Show that the ratio of the call price to the stock price is a martingale using the above measure. (3) Show that the ratio of the put price to the stock price is a martingale using the above measure. 3. Assume that a stock price is currently at $30. It is known that in one year stock price will be either $40 or $20. The annual interest rate is 5% with continuous compounding. Consider a European call option with strike price equal to $30 and 1 year to maturity and a European put option with strike price equal to $35 and 1 year to maturity. (1) What is the probability measure associated with stock being the numeraire? (2) Show that the ratio of the call price to the stock price is a martingale using the above measure. (3) Show that the ratio of the put price to the stock price is a martingale using the above measure