Kenneth is looking to price a 9-month European call option with a strike price of $19 on a share in ABC. The current price for an ABC share is $20. Kenneth has assumed the volatility of these shares to be 10% per annum. The risk-free continuously compounding interest rate is 5% per year.

a) Construct a 3-step binomial tree showing the possible share prices over the next 9 months. Also, clearly show the corresponding probabilities for an upward and a downward movement in the share price.

b) Using your binomial tree from part a) and the information given above, calculate the corresponding 3-step call option tree, and clearly state the fair price of the option according to the given information.

c) Estimate the Greek letters delta (), theta() and Gamma () from part a) and part b). You are NOT required to estimate vega () or rho ().