Question 6. (10 marks) Let S(t) be the share price at time t and let K be the exercise price of a European call option expiring at time T. Suppose S(t) has risen so far above K that the option is almost guaranteed to expire in the money. a. (5 marks) Using the Black Scholes formula (see L9.12 in the lecture notes) as a starting point, estimate the price of the option at time t. Explain your mathematical reasoning. b. (5 marks) Now suppose that the share price remains constant, i.e. S(t) S(T). How does the value of the option today differ from the final payout (is it larger or smaller)? Explain, referring to your estimate in part a, the reason for the difference. Some marks are associated with the clarity of your explanation