A stock is currently trading at $36.50 and has a volatility of 38% per annum and a continuous dividend yield of 4.00% per annum with continuous

compounding. The riskfree interest rate is 1.50% per annum with continuous compounding for all maturities. Given your expertise in stock option valuation you decide to use a fivestep binomial tree to calculate the following derivative prices (to four decimal places):

(a) A 10month European call option with a strike of $40.00. Calculate also the value of the option by using the BlackScholes formula. Compare the prices and comment.

(b) A 10month American call option with a strike of $40.00. Is the answer different to the answer from (a)? Explain why if so.

(c) A long position in a forward contract on the stock for delivery in 10 months at a price of $40.00. Calculate also the theoretical value of the forward position. Compare these values and comment. (Hint: the fair forward price that would be agreed for new contracts today is different to $40.00 and hence the forward contract in question has a nonzero value.)

(d) A European downandout barrier call option with a strike of $40.00 and knockout barrier of $35.00 maturing in 10 months. A downandout call option gives the holder the right to buy the underlying asset at the strike price on the expiration date so long as the price of that asset did not go below a predetermined barrier during the option's lifetime. When the price of the underlying asset falls below the barrier, the option is "knockedout" and

no longer carries any value. Comment on the price of this option relative to the option in (a) and explain any differences. Would the value of this option change if the knockout barrier was lowered from $35 to $32? Comment on the reason why.

Please answer all questions and use Excel if necessary.