Consider a two-step binomial tree for a European put option on a non-dividend paying stock XY. The current price of stock XY is $60. Over each of the next two 6-month periods the stock price is expected to go up by 10% or down by 10%. The risk-free rate of interest is 8% per annum with continuous compounding. The European put option will expire in 1 year and has an exercise price of $55.

a) Calculate the probabilities that the stock price goes up and down in the risk neutral world. [4 marks]

b) Calculate the stock price at each node of the binomial tree. [7 marks]

c) Use the binomial option pricing formula to calculate the value of the put option at each node of the tree. [12 marks]

d) Can you explain why, in your calculations of the option price, you are allowed to use the risk-free rate of interest? [7 marks]