An option pricing model that is most commonly used is the Black-Scholes model, but there is also the Monte Carlo method for pricing options. Both of these mathematical models try to create a standardized way to evaluate the risk associated with equity options, and in particular American style options, and quantify that risk in order to determine the price.
This article will touch on very generic concepts related to these traditional option pricing models. Given the complexity of these formulas, you should seek additional sources to supplement or complete your understanding of these option pricing models and how they work.
What are Equity Options?
It is important to begin by establishing a basic understanding about options and what they do. An option is a contract that is issued on and derives its value from some underlying asset. In the case of equity options (which is what will be discussed in this article) the underlying asset is a listed stock and certain over the counter stock that is permitted to issue options. The price of the stock at the time the option is created, coupled with expected movement of that stock, are factors that determine the pricing for the option.
There are 2 basic types of options, calls and puts. A call is an option contract that when exercised calls the stock away from its owner at some predetermined price, known as the exercise or strike price. Calls are typically purchased when a stock is rising. A put option gives the buyer of the option the opportunity to sell the stock at the strike price. It is usually purchased when the investor feels that the stock market is going down. The purchase price for either a call or put is known as the premium. The premium is determined based on the price of the stock relative to the strike price of the option. The further the strike price of the option is from the underlying stock price, the less expensive it is.
Black Sholes Pricing Model
The Black Sholes pricing model was developed to create a mathematical way to compare the market value of a stock with its theoretical value. This comparison resulted in a consistent way to establish the risk pricing for models and the difference between a hedge to the upside (using calls), or a hedge to the downside (using puts). The model uses a set of assumptions to determine how to price options, including:
- the stock pays no dividends
- the option can only be exercised at its expiration date
- the direction of the market cannot be predicted (random walk theory)
- interest rates remain the same or constant
- there is no commission
- the distribution of returns is normal and volatility is constant
Monte Carlo Method for Options Pricing
The Monte Carlo method for options pricing takes the Black Sholes method a step further. It looks at additional levels of risk or uncertainty that can affect the overall risk to a stocks price. These additional factors produces a more accurate reflection of what a stock may do, thus creating a truer predictor of an options price.