Shares of Scruggs Inc. are currently trading at $27 with volatility of returns of 22% per annum. The annual continuously compounded risk-free rate of interest is 2%.

(a) Use the Black Scholes option pricing model to price a 3-month European-style put option written on Scruggs Inc. with an exercise price of $30 and interpret your findings. (30 marks)

(b) Every month, the share price is expected either to increase, by a multiplicative factor of u = 1.1, or decrease. Construct a binomial tree to price the option if it is American-style, discuss the process and interpret your findings. (30 marks)

(c) Scruggs Inc. features in the FLATT500 stock index, which pays a continuous dividend yield of 1.2%, has a contract multiplier of $100 per full index point and volatility of returns of 20% per annum. Calculate the price of a five-month at-the-money European- style call option when the index is at 2,500 points and interpret your findings. (40 marks)