A Multivariate Stochastic Volatility Model Applied to a Panel of S&P500 Stocks in Different Industries

• Date: 01 September 2017
• Author: Thanasis Stengos,Serda S. Öztürk
• Published date: 01 September 2017
• DOI: http://doi.org/10.1111/irfi.12111

A Multivariate Stochastic Volatility

Model Applied to a Panel of S&P500

Stocks in Different Industries

SERDA S. ÖZTÜRK

†

AND THANASIS STENGOS

‡

†

Istanbul Bilgi University, Istanbul, Turkey and

‡

Economics and Finace, University of Guelph, Guelph, Canada

ABSTRACT

We estimate a multivariate stochastic volatility model for a panel of stock

returns for a number of S&P 500 f‌irms from different industries. To directly

compare our results with those from the univariate estimation literature on

the same data, we use an eff‌icient importance sampling (EIS) method to esti-

mate the likelihood function of the given multivariate system that we analyze.

As opposed to univariate methods where each return is estimated separately

for each f‌irm, our results are based on joint estimation that can account for

potential common error term interactions based on industry characteristics

that cannot be detected by univariate methods. Our results reveal that there

are important differences in the industry effects, something that suggests that

differential gains to portfolio allocations in the different industries that we

examine. There are differences because of idiosyncratic factors and the

common industry factors that suggest that each industry requires a separate

treatment in arriving at portfolio allocations.

JEL Codes: G170; C150

1. INTRODUCTION

Asset volatility has been an area of intense research in f‌inance and f‌inancial

econometrics in the last three decades. The seminal work of Engle (1982) who

introduced the ARCH-type models has been one of the main vehicles to study

and model volatility as a conditional moment of interest that needs estimating

in the same way as the conditional mean that def‌ines the typical regression func-

tion needs to be estimated. In their generalized (GARCH) form, these models

assume that conditional variances are functions of past variances and/or past

squared returns. At the same time, stochastic volatility (SV) models, introduced

by Taylor (1982, 1994), offer an important alternative to ARCH-type models

and are the focus of our paper. Under SV, volatility follows a stochastic process

generally independent of the conditional mean process. In GARCH-type models,

the conditional variance of returns is assumed to be a deterministic function of

past returns, whereas in SV models the volatility process is random. The

© 2017 International Review of Finance Ltd. 2017

International Review of Finance, 17:3, 2017: pp. 479–490

DOI: 10.1111/irf‌i.12111