3. [3] (a) Within the Binomial Tree model, describe the dynamic of the spot price and explain the risk-neutral valuation approach to valuing a European option using a one-step binomial tree. (b) Explain carefully the difference between selling a call option and buying a put option. Write down the two payoffs and draw their graphs. (e) A stock price is currently 37 . Over each of the next two three-month periods it is expected to go up by 12% or down by 8%. The risk free interest rate is 1% per annum with continuous compounding. 6) What is the value of a six-month European put option on the underlying stock with a strike price of 41 ? (ii) What is the value of a six-month American put option on the underlying stock with the same strike price? (iii) Explain briefly what the delta of a stock option is. [2] (iv) Calculate the delta over each step for part 3(e)i. (v) Compute the price of a European call with the same underlying, strike price and maturity of the put in 3(c) using the put-call parity, [3] [5]