What is Historical Volatility in Options Trading?

The historical volatility of an underlying asset underlying the option, such as a stock or an index, describes the range of fluctuation of the price in the past. Historical volatility can be used to describe the risk or potential for downward and upward price fluctuations.

However, the historical volatility of an underlying asset is of secondary importance for the valuation of options. The implicit volatility, i.e. the expected fluctuation range over the remaining term of the option, is the main factor taken into account. However, the historical volatility has an influence on the implied volatility to a certain extent.

In addition to the implicit volatility, other factors such as the remaining term to maturity, the current price of the underlying, the strike price and the interest rate prevailing on the market are also taken into account in the pricing and thus valuation of options. Although historical volatility has an indirect influence, it is not of decisive importance.

The significance of historical volatility

Historical volatility describes a certain statistical potential with which an underlying asset can move up or down from its average value over a certain period of time.

In the past, for example, an underlying asset was always highly susceptible to upward or downward movements. It can therefore be concluded with some probability that this could also be the case in the future.

In other words, it is clear to every equity investor that there are equities with high overall volatility and equities with low volatility. In many cases, this is also interpreted to mean the risk of a share.

The average historical volatility of the last 180 days was 20%. The figure for the last ten days was 40%. From this it can be concluded that investors trade the stock with a significantly higher volatility than normal.

However, the historical volatility cannot be readily used to value options. Various factors are responsible for this. These include, for example, the remaining term of the option and market participants’ expectations for the future.

If the remaining term is rather short, the underlying stock usually no longer has the “chance” to develop its full fluctuation potential. The results from the observation of historical volatility are of little help here.

There are simply too few days left for historically observed fluctuations, such as those of the past three months, to have such an impact on the underlying asset that they still have a decisive influence on the value of an option or the corresponding performance of the underlying asset.

Factors influencing the option price

The price of options results from many different factors like:

  • current price of the underlying asset
  • Term of the options
  • Exercise price
  • riskless interest
  • implied (expected) volatility

Historical vs. implied volatility

The implied volatility is used to estimate the potential fluctuation of an underlying asset in relation to one year. The observed historical volatility is taken into account to a certain extent. First, the daily fluctuation potential of the share is determined. To a certain extent, this can also result from past observations.

An implied volatility of 24 % means an expected, i.e. future, fluctuation margin of 24 %, based on one year. This value is divided by 16. This is the root of the number of trading days in a year. The basis is 256 trading days. The calculation results from the formula for determining the standard deviation. The result is an implied volatility of 1.5% on a daily basis.

Statistically speaking, the share price could therefore change by 1.5 % upwards or 1.5 % downwards every day within the remaining term to maturity. For very short remaining terms, an out-of-the-money option offers little opportunity to build up a large intrinsic value and thus profit. This is true even if large fluctuations within a certain period of time were observed in the past.


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