Stochastic methods in applied finance:

Alex is looking to price a 6 month European put option with a strike price of $29 on a share in Omni Consumer Products (OCP). The current price for an OCP share is $20. Alex has used past data and his own judgement to estimate the volatility of these shares to be 15% 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 6 months. Also, clearly show the corresponding probabilities for an upward and a downward movement in the share price.

As a check, the numbers 26.5419 and 31.8945 should appear in your tree.

(b) Using the binomial tree in part (a) and the information given above, calculate the corresponding 3 step tree containing the corresponding option values, and clearly state the fair price of the option according to the given information.

As a check, the numbers 0.157 and 0.7820 should appear in your tree.

c) Using the binomial tree constructed in part b), estimate the time zero (t = 0) values of delta (A), theta (0), and gamma () ONLY. You do NOT need to calculate nu (v) and rho (p)