13. Shares of Haggard Inc. are currently trading at $45 with volatility of returns of 20% per annum. The annual continuously compounded risk-free rate of interest is 1.5%. (a) What, according to the Black Scholes option pricing model, will be the price of a 3- month European-style put option on Haggard Inc. with an exercise price of $50? (30 marks) (b) Every month, the share price is expected either to increase, by a multiplicative factor of u = 1.1, or decrease. What will the price of the put option be if it is American-style? (30 marks) (c) Discuss the impact on the Black Scholes price in part (a) and the binomial trees in part (b) if Haggard Inc. was expected to pay a dividend of $5 with 1 month remaining until the option's maturity. (40 marks)