A Class of Nonlinear Stochastic Volatility Models

Univ. of Auckland, Economics Working Paper No. 229

33 Pages Posted: 4 May 2002

See all articles by Jun Yu

Jun Yu

Singapore Management University; Singapore Management University - Lee Kong Chian School of Business

Zhenlin Yang

Singapore Management University

Date Written: April 18, 2002

Abstract

This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling stochastic volatility. The efficient method of moments approach is used to estimate model parameters. Empirical results reveal that the lognormal stochastic volatility model is rejected for daily index return data but not for daily individual stock return data. As a consequence, the stock volatility can be well described by the lognormal distribution as its marginal distribution, consistent with the result found in a recent literature (cf Andersen et al (2001a)). However, the index volatility does not follow the lognormal distribution as its marginal distribution.

Keywords: Box-Cox Transformation, GARCH, EMM, Stochastic Volatility

JEL Classification: G12, C22, C52

Suggested Citation

Yu, Jun and Yang, Zhenlin, A Class of Nonlinear Stochastic Volatility Models (April 18, 2002). Univ. of Auckland, Economics Working Paper No. 229, Available at SSRN: https://ssrn.com/abstract=307731 or http://dx.doi.org/10.2139/ssrn.307731

Jun Yu (Contact Author)

Singapore Management University ( email )

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Singapore Management University - Lee Kong Chian School of Business ( email )

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Zhenlin Yang

Singapore Management University ( email )

School of Economics
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Singapore
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HOME PAGE: http://www.mysmu.edu/faculty/zlyang/

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