
Time-Varying Volatility
Time-varying volatility refers to the fluctuations in volatility over different time periods. 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. 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. Time-varying volatility describes how the price volatility of an asset may change given different time periods. Overall, options with a longer time to expiration will have a higher volatility while options expiring in a shorter amount of time will have a lower implied 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 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.



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 mathematic 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 backwards 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 a higher volatility while options expiring in a shorter amount of time will have a 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.
Related terms:
Autoregressive Conditional Heteroskedasticity (ARCH)
Autoregressive conditional heteroskedasticity is a time-series statistical model used to analyze volatility in high frequency data. read more
Black-Scholes Model
The Black-Scholes model is a mathematical equation used for pricing options contracts and other derivatives, using time and other variables. read more
Heston Model
The Heston Model, named after Steve Heston, is a type of stochastic volatility model used by financial professionals to price European options. read more
Historical Volatility (HV)
Historical volatility is a statistical measure of the dispersion of returns for a given security or market index realized over a given period of time. read more
Implied Volatility (IV)
Implied volatility (IV) is the market's forecast of a likely movement in a security's price. It is often used to determine trading strategies and to set prices for option contracts. read more
Lattice-Based Model
A lattice-based model is a model used to value derivatives; it uses a binomial tree to show different paths the price of the underlying asset may take. read more
Local Volatility (LV)
Local volatility (LV) is a volatility measure used in quantitative analysis that provides a more comprehensive view of risk when pricing options. read more
Security : How Securities Trading Works
A security is a fungible, negotiable financial instrument that represents some type of financial value, usually in the form of a stock, bond, or option. read more
Standard Deviation
The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. read more
Technical Analysis of Stocks and Trends
Technical analysis of stocks and trends is the study of historical market data, including price and volume, to predict future market behavior. read more