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

Peter Christoffersen, Kris Jacobs and Karim Mimouni (pchristoffersen@creates.au.dk)
Additional contact information
Karim Mimouni: School of Economics and Management, University of Aarhus, Denmark and CREATES, Postal: 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on S&P500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, 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 errors in- and out-of-sample.

Keywords: Stochastic volatility; option valuation; particle filtering; skewness; kurtosis; mean reversion (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Pages: 37
Date: 2007-11-15
New Economics Papers: this item is included in nep-fmk
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/07/rp07_37.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2007-37

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by (bhoejklint@econ.au.dk).