Actuarial Math/ Financial Math Problem: Binomial Tree Pricing Model

Problem 1 (Required, 25 marks) (a) We consider an American put option on a non-dividend paying asset. Prove that when the interest rate is 0 (i.e. r = 0), it is always not optimal to exercise before the maturity date. (b) We consider an American call option on an asset with strike price X and maturity date T (where T > t). The asset pays dividend continuously at an annual dividend yield rate q. Show that if it is optimal for the investor to exercise the option now, then the dividend yield rate q should satisfy 1 X(1-e - In 1 T-t St Here, r is the annual nominal interest rate and St is the asset price at current time t. q> Problem 1 (Required, 25 marks) (a) We consider an American put option on a non-dividend paying asset. Prove that when the interest rate is 0 (i.e. r = 0), it is always not optimal to exercise before the maturity date. (b) We consider an American call option on an asset with strike price X and maturity date T (where T > t). The asset pays dividend continuously at an annual dividend yield rate q. Show that if it is optimal for the investor to exercise the option now, then the dividend yield rate q should satisfy 1 X(1-e - In 1 T-t St Here, r is the annual nominal interest rate and St is the asset price at current time t. q>