Question:

ZZZ stock is trading at $250 with an annual volatility of return 20%. The expected stock return is 12% and the annual risk-free rate of interest is 8%. The stock does not pay any dividends. (Note: using Excel to answer this question may save you some time)

a) (2 point) Using Black-Scholes formula, find the price of 3-month European call option with strike price of $250?

b) (2 point) Using Black-Scholes formula, find the price of 3-month European put option with strike price of $250?

c) Now, lets divide the 3-month interval into 10 equal length intervals and consider a 10-step Binomial option pricing model with Cox-Ross-Rubenstein assumptions for the stock behavior in each step

c.1) (2 points) Write down u, d, and risk-neutral probability p for this model (keep 6 decimal digits!)

c.2) (2 point) Using this model, find the price of 3-month European put option with strike price of $250

d) Assume that ZZZ has decided to pay dividends and assume (although not very realistic assumption) that these dividends are paid continuously with continuously compounded dividend yield of 5%. Assume also that no production changes are made (e.g., assume that such dividends substitute the stock repurchase program that ZZZ had in the past)

d.1) (1 points) What will be the new annual volatility of stock return?

d.2) (2 points) regardless of your answer in part (d.1), assume the annual volatility of stock returns remains the same 20%. Using Black-Scholes formula, find the price of 3-month European call option with strike price of $250.