The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding.

a) What is the option price when u = 1.1 and d = 0.9 using risk neutral valuation?

b) Verify that using the delta hedging method gives you the same answer.

c) Explain the reasons why delta is different at each node.

(note: you need to show workings, but please draw the tree, and write the option price and delta at each node of the tree to summarise your answer)