Question

A 3-month American call option on a stock has a strike price of $20. The stock price is $20, the risk-free rate is 3% per annum, and the volatility is 25% per annum. A dividend of $1 per share is expected at the end of the second month. Use a three-step binomial tree to calculate the option price.

Answer 1

The binomial tree is given in the diagram above with the working. T1 is the first month, T2 second month and T3 third month.

As this is a call option .. the price of option will be Spot price -(minus) Strike price. For e.g at the end of First month (T1) month the Price increase at $25 will have the call option price to be $25 (spot price)-$20(stike price)= $5. so on for each time frame.

If at end of any time frame the spot price is lesser than the strike price the option price will be zero.