# How Options Are Priced

07/09/2013 8:00 am EST

**Focus:** OPTIONS

*You don't need to have an advanced math degree in order to trade options, but it's important to understand the inputs that go into option pricing, writes Marcus Holland of Options-Trading.com.*

Options are derivative securities that provide the buyer of an option with the right but not the obligation to purchase or sell an underlying security, such as a stock, on or before specific date. The pricing of options has changed over the years but the benchmark known as the Black-Scholes options pricing model is still used to price stock options as well as many other securities such as commodities and currencies.

The model was first articulated by Fischer Black and Myron Scholes in their 1973 paper, *The Pricing of Options and Corporate Liabilities*. The idea behind their model as well as most options pricing models is to determine, based on a number of inputs, the value of security at any given time. The main inputs used in the Black-Scholes model are the strike price of the option, the current underlying price of the security, the time to maturity, current interest rates, and implied volatility.

The Black-Scholes equation is a partial differential equation, which describes the price of the option over time. The equation is relatively sophisticated but most traders do not need to understand the specifics of the math, but need to be in tune to the inputs that are used to generate an option value. The equation is:

**Inputs**

The strike price of an option is the price where the buyer can exercise the option and purchase or sell the underlying security. For example, a crude oil July 100 call option will allow the buyer of the option to purchase crude oil at $100 per barrel.

The underlying price at the time of the purchase of the option is important. If crude oil in the example above is $110 per barrel, then the option is in the money and will have a value that includes $10 dollar of intrinsic value. If the price on the other hand is $90 per barrel, the value of the option is purely time value and price based on the chance that crude oil will move higher by more than $10 per barrel and expire in the money.

The time to maturity is the amount of time left prior to the expiration of the option. The longer the time to maturity of an option contract, (all other inputs remaining unchanged) the greater the value of the option. For example, a crude oil December 2013, 100 (strike) call option will be more expensive than a July 2013, 100 call option.

Interest rates have an effect on the value of an option as higher interest rates increase the time value of money. The higher the interest rate used to calculate the value of an option, the more expensive the option value.

The most important input into an option is generally the implied volatility, which is an estimate used by market participants to determine how much a security will move over a certain period of time on an annualized basis. Higher levels of implied volatility equate into higher options prices.

The Black-Scholes model is the benchmark for most option pricing models, but the inputs into this model are the driving force behind the price of an option.

**By Marcus Holland, Editor, Options-Trading.com**