# Binomial Method

• Binomial method entails
• Assuming the price of the underlying asset can take only two values in any given interval of time
• Determining Option pay-offs at these prices
• Replicating the same pay-offs in a package consisting of assets that can be valued
• Alternatively, determining probability of each pay-off to arrive at a certainty equivalent expected cash-flow and discounting it to the present value at the risk-free rate
• Risk Neutral Method

# An Example

Question:

Consider a six-month European call and put option on non-dividend paying stock with identical exercise prices of Rs 85. This option is at the money. The short-term, risk-free interest rate was a bit less than 4 percent per year, or about 2 percent for six months. The stock either falls to Rs 63.75 or rises to Rs113.33 after six months. Determine their pay-offs at expiration:

Solution:

The pay-offs are as follows:

 Stock Price = Rs. 63.75 Stock Price = Rs.113.33 1 Call option Rs. 0 Rs. 28.33 1 Put option Rs. 21.25 Rs. 0