# Time-Varying Volatility

## What Is Time-Varying Volatility?

Time-varying volatility refers to the fluctuations in volatility over different time periods. Investors may choose to study or consider the volatility of an underlying security during various time periods. For instance, the volatility of certain assets may be lower during the summer when traders are on vacation. The use of time-varied volatility measures can influence the expectations of investments.

### Key Takeaways

• Time-varying volatility describes how the price volatility of an asset may change given different time periods.
• Volatility analysis requires the use of financial models to resolve statistical differences in price fluctuations over different time-frames.
• Volatility tends to be mean-reverting, therefore periods of high volatility may be followed by periods of low, and vice-versa.

## How Time-Varying Volatility Works

Time-varying volatility can be studied in any time frame. Generally, volatility analysis requires mathematical modeling to generate volatility levels as one measure of the risk of an underlying security. This type of modeling generates historical volatility statistics.

Historical volatility is generally referred to as the standard deviation of prices for a financial instrument, and hence a measure of its risk. Over time a security is expected to have varying volatility subject to large swings in price, with stocks and other financial instruments exhibiting periods of high volatility and low volatility at various points in time.

Analysts may also use mathematical calculations to generate implied volatility. Implied volatility differs from historical volatility in that it is not based on historical data but rather a mathematical calculation that provides a measure of the market’s estimated volatility based on current market factors.

## Historical Volatility

Historical volatility can be analyzed by time periods based on the availability of data. Many analysts seek to first model volatility with as much available data as possible in order to find the volatility of security over its entire life. In this type of analysis, volatility is simply the standard deviation of a security’s price around its mean.

Analyzing volatility by specified time periods can be helpful for understating how a security has behaved during certain market cycles, crises, or targeted events. Time series volatility can also be helpful in analyzing the volatility of a security in recent months or quarters versus longer time-frames.

Historical volatility can also be a variable in different market pricing and quantitative models. For example, the Black-Scholes Option Pricing Model requires the historical volatility of a security when seeking to identify its option price.

## Implied Volatility

Volatility can also be extracted from a model such as the Black-Scholes model to identify the market’s current assumed volatility. In other words, the model can be run backward taking the observed market price of an option as the input to impute what the volatility of the underlying asset must be in order to achieve that price.

Generally, implied volatility’s time frame is based on the time to expiration. Overall, options with a longer time to expiration will have higher volatility while options expiring in a shorter amount of time will have lower implied volatility.

## The 2003 Nobel Prize in Economics

In 2003 economists Robert F. Engle and Clive Granger won the Nobel Memorial Prize in Economics for their work in studying time-varying volatility. The economists developed the Autoregressive Conditional Heteroskedasticity (ARCH) model. This model provides insight for analyzing and explaining volatility over different time periods. Its results can then be used in predictive risk management which can help to mitigate losses in a variety of different scenarios.