# What is the Binomial Option Pricing Model?

Jim B.

The binomial option pricing model is a method for determining the value of an options contract, a contract that provides the owner with the exclusive opportunity to purchase or sell some asset for an agreed-upon price during a predetermined time time frame. This model is helpful to investors because it is difficult to pinpoint the value of an options contract, which is based on the price of some underlying instrument. In addition, the binomial option pricing model, or BOPM, is especially useful for American options, which can be exercised at any point before the expiration date. A typical BOPM is set up like a tree, with the original price giving way to two prices, which gives way to three, and so on.

Options contracts give investors the opportunity to speculate on the price of an underlying security without actually gaining physical ownership of the asset. Since the contract's value is based on the value of the underlying asset at some future time, it is difficult for an investor to assess the value of the contract at the time of purchase. One method of projecting options prices into the future is the binomial option pricing model, which can nail down a set of possible values for a contract, based upon the underlying asset's prices, from its inception to its expiration.

For the binomial option pricing model to be successful, one must be able to gauge the volatility of an asset, which is the degree to which the price of the underlying asset can shift within a limited time frame. As an example, imagine an asset has a current price of \$100 US Dollars (USD) and it has a volatility level of 20 percent. That means that the price of the asset for the second period judged by the BOPM would be \$120 USD if the price goes up, or \$80 USD if the price goes down.

In the next step, these two prices would be further broken down based on volatility to produce three more possible prices for the following period. In the characteristic branching structure of BOPM, three possible prices would split into four, and so on for the duration of the option. This allows investors to make very specific predictions about their assets' possible future prices. Another benefit of the binomial option pricing model is that it can be adjusted to reflect anticipated changes based on the likelihood of a price moving either up or down. In the example above, it was assumed there was a 50 percent chance of the price going up and a 50 percent chance of it going down into the second period. But in the next period, those percentages could be affected by the price turns an asset generally takes. The BOPM can account for this.

Along with providing a good valuation model for options, the binomial option pricing model can help the holders of American options decide when to exercise those options. If the BOPM showed the potential future prices for an underlying asset to be exceptionally high, an investor might want to hold on to the option. On the other hand, prices taking a downward spiral on the model could cause the investor to exercise the option at its peak value.