Problem 2: Option Valuation (18 marks) LAST DIGIT : 4 In this question, you need to price options with various approaches. You will consider puts and calls on a share. Please read following instructions carefully: The spot price of this share will be determined by your student number. You need to use the last digit of your student number. The spot price of the share will be (last digit of your student number10+6). For example, if the last digit of your student number is 5, the spot share price will be 510+6=56. If the last digit of your student number is 0, please replace it with 4, i.e. the spot price will be 4*10+6=46. The strike price of the options will be the share price you just calculated +2. For example, if the share price you calculated based on your student number is 56, the strike price of the options will be (56+2)=58. Based on this spot price and this strike price as well as the fact that the risk-free interest rate is 6% per annum with continuous compounding, please undertake option valuations and answer related questions according to following instructions:

Additionally, assume that over each of the next two four-month periods, the share price is expected to go up by 11% or down by 10%. a. Use a two-step binomial tree to calculate the value of an eight-month European call option using the no-arbitrage approach. [2.5 marks]

b. Use a two-step binomial tree to calculate the value of an eight-month European put option using the no-arbitrage approach. [2.5 marks]

c. Show whether the put-call-parity holds for the European call and the European put prices you calculated in a. and b. [1 mark]

d. Use a two-step binomial tree to calculate the value of an eight-month European call option using risk-neutral valuation. [1 mark] e. Use a two-step binomial tree to calculate the value of an eight-month European put option using risk-neutral valuation. [1 mark] f. Verify whether the no-arbitrage approach and the risk-neutral valuation lead to the same results. [1 mark]

g. Use a two-step binomial tree to calculate the value of an eight-month American put option. [1 mark]

h. Calculate the deltas of the European put and the European call at the different nodes of the binomial three. [1 mark]

Note: When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the different nodes of the binomial tree.