Barry wants to purchase a 1-year European call option on ABC shares with a strike price of $30. The current price for an ABC share is $27. Barry estimates the volatility of these shares to be 13% per annum. The risk-free continuously compounding interest rate is 3% per year.

a) Construct a 3-step binomial tree showing the possible share prices over the next year. 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) Using the binomial tree constructed in part b), estimate the time zero ( = 0) values of delta (), theta (), and gamma () ONLY. You do NOT need to calculate nu () and rho ().