Options volatility

There are two types of volatility:

• Historical volatility, also called realized volatility, is the backward-looking measure of volatility. It measures the level of price fluctuations in the past by looking at the historical price movement.
• Implied volatility is the forward-looking measure of volatility. In the case of options, the implied volatility is ‘implied’ from their price and reflects the market’s expectation of the volatility of the option’s underlying asset from now until the expiration of the option.

Implied volatility is one of the inputs used in option pricing models, e.g. the Black-Scholes model, along with the price of the underlying asset, the option’s strike price, its expiration date, the interest rate and dividends. Most of these inputs can be readily observed in the market, but the implied volatility can’t. Using the market price of the option, it is possible to reverse engineer an option pricing model to find out what level of implied volatility is priced in. The other exception is the dividend, which in normal conditions can be determined ahead of time with relative certainty. Unexpected deviations can, however, have a large impact on option prices.

Example

If the shares of Airbus Group are trading at €100 and the implied volatility of an option contract on this share is 15%, then a one standard deviation move over the next 12 months will be plus or minus €100 * 15% = €15.

In theory, it is assumed that the share price follows a normal distribution. This implies that, after one year, the share could end up within one standard deviation of its original price 68% of the time, with a 32% chance the share price will be outside this range.

As such, the implied volatility of 15% means the market’s current expectation is that there is a 68% chance the share price will end up between €85-115 in a year from now.

If the implied volatility were to rise to 20%, there would be a 68% chance the share price would end up between €80-120 and 32% chance it would be outside this range. As the likelihood of the share price deviating further from the strike prices increases, the option contract typically increases in value. If the option’s vega is 0.5, the implied volatility increases from 15% to 20% would result in the option’s price rising by 5 * 0.5 = €2.50.