Question

Binomial Model and Option Pricing

The shares of XYZ Inc. are currently selling for $120 per share. The shares are expected to go up by 10 percent or down by 5 percent in each of the following two months (Month 1 and Month 2). XYZ Inc. is also expected to pay a dividend yield of 2 percent at the end of Month 1. The risk-free rate is 0.5 percent per month.

a.        What is the value of an American call option on XYZ shares, with an exercise price of $125 and two months to expiration? Use the binomial model to obtain the answer.

b.      Draw a binomial tree diagram for this American call option, showing the share price, call price, and whether the call should be exercised at each state during the next two months.

Answer 1

• First calculate the future spot price at each node.
• Next would be to calculate the call option value at t=1 by comparing future spot prices with strike price at each node
• Calculate the value of call option at t=2 and find the value of option at t=1 by discounting using the risk free rate
• Compare this present value to the call option value calculated using step 2
• Whichever value is the higher of the two must be considered
• The higher value is then discounted to t=0, and the call option value is arrived at.

Please check images for the complete calculations and the binomial model diagram. Give a thumsup if you are happy with the solution. Cheers