Volatility of S&P500: Estimation and Evaluation

TL;DR

This paper compares different methods for estimating S&P 500 volatility, finding implied volatility to be most accurate and recommending specific window adjustments for historical and GARCH models.

Contribution

It evaluates and compares multiple volatility estimation methods and window adjustments, providing practical recommendations for risk management.

Findings

Implied volatility best estimates real volatility.

Rolling window preferred for historical volatility.

Increasing window suitable for GARCH model.

Abstract

In an era when derivatives is getting popular, risk management has gradually become the core content of modern finance. In order to study how to accurately estimate the volatility of the S&P 500 index, after introducing the theoretical background of several methods, this paper uses the historical volatility method, GARCH model method and implied volatility method to estimate the real volatility respectively. At the same time, two ways of adjusting the estimation window, rolling and increasing, are also considered. The unbiased test and goodness of fit test are used to evaluate these methods. The empirical result shows that the implied volatility is the best estimator of the real volatility. The rolling estimation window is recommended when using the historical volatility. On the contrary, the estimation window is supposed to be increased when using the GARCH model.