Question

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.

Answer 1

Upward price movement factor(u)=1.1

downward price movement factor (d)=(1-5%)=0.95

Interest factor= 1.005

Upward price movement probability= (1.005-0.95)/(1.1-0.95)=36.67%

Downward price movement probability=(1-36.67%)=63.33%

At the end of Month 1 price of share can be either 120*1.1 or $132 or 120*0.95=$114

However, Dividend after month 1= 2%*120=$2.4

So, price of share after month 1 is either (132-2.4)=$129.6 or (114-2.4)=$111.6

Hence, price after Month 2 from price 129.6 will be either 129.6*1.1=142.56 or 129.6*0.95=$123.12

Similarly price after month 2 from price $111.6 will be either 111.6*1.1=122.76 or 111.6*0.95=106.02

Except for price, $129.6 and 142.56, in all other cases option will be expired.

Expected Payoff at price 142.56 at the end of month 1= (142.56-125)=$17.56*36.67%/1.1=5.85 and payoff at price 129.6= (129.6-125)=4.6

Present Value of payoff at Month 0= 5.85*36.67%/1.1=$1.95

a. So, Value of American call option is $1.95