As we discussed yesterday in The Layman's Guide to Natural Gas Options - Part II, there are four primary variables that affect the premium or price of natural gas, as well as crude oil, heating oil and gasoline, options:

• The prevailing price of the underlying natural gas swap relative to the strike price of the option
• The time remaining until the option expires (also known as theta)
• Price volatility of the underlying natural gas swap
• Interest rates

Yesterday we focused on the second variable, the time value of an option. Today we're going to address another major component of the price of natural gas options, volatility.

Volatility is an important factor in the pricing of options. In fact, volatility is the key component to pricing an option as it is the only "unknown" variable in an option pricing model. Given an options market price and knowing the other variables in the pricing model - the price of the underlying future or swap, the strike price, the time to expiration and interest rate - the remaining factor - the derived volatility - is implied by the option's price.

As natural gas prices fluctuate, the premium for a natural gas option will increase as the probability of options attaining intrinsic value or moving deeper into the money increases. As such, option sellers demand higher premiums for options when volatility is or is anticipated to be "high" and vice versa.

Historical volatility is calculated from the past movement of natural gas prices over a specified time period. Mathematically, historical volatility is computed as the standard deviation of the log of the changes in natural gas futures and swaps prices price, expressed in percentage terms, annualized.

To put it another way, if the implied volatility of a natural gas option is 50%, it means that there is a 68.3% chance (one standard deviation) that a year from now, the underlying price (future or swap) of that option will be 50% higher or lower. Historical volatility is important because many traders use it as a tool for forecasting future volatility.

As mentioned previously, volatility is the most important variable of an option's price. As a hypothetical example, the price of a $4.00 NYMEX natural gas put option with 150 days to expiration might currently trade for 24¢, based on a volatility of 50%, while the same option with volatility of 25% might trade for as little as 12¢.

So, what does volatility mean to a producer or consumer looking to hedge natural gas with options? In essence, it means that during periods of high implied volatility you will pay more for an option than you would pay for the exact same option during periods of low implied volatility.

UPDATE: This post is the first in a series on natural gas options.  The previous and subsequent posts can be found via the following links:

The Layman's Guide to Natural Gas Options - Part I - Price

The Layman's Guide to Natural Gas Options - Part II - Time Value

The Layman's Guide to Natural Gas Options - Part IV - Interest Rates