# Time-Varying Oscillations

What is the time-varying volatility

Time-varying volatility is the fluctuation of volatility in different periods of time. Investors can choose to study or to consider the volatility of assets in different time periods. The use of time-is a measure of volatility can affect the expectations of the investment.

Breaking down the ‘time-varying volatility’

Time-varying oscillations can be studied on any time frame. Generally, the volatility analysis requires mathematical modelling to generate levels of volatility as a risk measure of the underlying asset. This type of simulation generates statistics historical volatility.

Historical volatility usually is called the standard deviation of the price of a financial instrument, and therefore a measure of its risk. Over time safe have different volatility are subject to greater fluctuations in price, with stocks and other financial instruments exhibiting periods of high volatility and low volatility at various points in time.

Analysts can also use mathematical calculations to generate the implied volatility. Implied volatility is significantly different from the historical volatility that it is not based on historical data, a mathematical calculation which allows to determine the approximate market volatility based on current market factors.

Historical Volatility

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

Analyzing volatility, these time periods may be useful for understanding how security behaved in certain market cycles, crises or deliberate events. The volatility time series can also be useful in the analysis of the volatility of the securities over the last months or quarters compared to the longer term.

Historical volatility may also be variable in different market pricing and quantitative models. For example, black-Scholes requires the historical volatility of security, when seeking to determine your price.

Implied Volatility

Volatility can also be extracted from a model such as black Scholes to determine the current implied volatility of the market. The terms generally implied volatility is based on the time until the end. In General, options with longer time to expiration will have a higher volatility and option which expire in a short period of time will have a lower volatility.

Nobel Laureate 2003

Economists in a 2003 Robert F. Engle and Clive Granger received the Nobel prize in Economics for their work on the study of time-varying volatility. Economists have developed Autoregressive conditional Heteroscedasticity model (arch). This model provides knowledge for the analysis and explanation of volatility for different time periods. Then the results can be used in a predictive risk management, which can help to reduce the losses in various scenarios.