Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns and Option Prices

49 Pages Posted: 24 Aug 2006 Last revised: 25 Sep 2009

See all articles by Peter Christoffersen

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Kris Jacobs

University of Houston - C.T. Bauer College of Business

Karim Mimouni

McGill University - Desautels Faculty of Management

Date Written: July 31, 2007

Abstract

Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases.

We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources: realized volatilities, S&P500 returns, and an extensive panel of option data. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. The best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance, which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared error in- and out-of-sample. It fits the option data better than the SQR model in several dimensions: it improves the fit of at-the-money options, and it provides a more realistic volatility term structure and implied volatility smirk.

Keywords: Stochastic volatility, option valuation, particle filtering, skewness, kurtosis, mean reversion

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Jacobs, Kris and Mimouni, Karim, Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns and Option Prices (July 31, 2007). EFA 2007 Ljubljana Meetings Paper; AFA 2008 New Orleans Meetings Paper. Available at SSRN: https://ssrn.com/abstract=926373 or http://dx.doi.org/10.2139/ssrn.926373

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
Canada
416-946-5511 (Phone)

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Kris Jacobs

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

Karim Mimouni

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

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