Abstract

A class of stochastic volatility (SV) models is proposed by applying the Box–Cox transformation to the volatility equation. This class of nonlinear SV (N-SV) models encompasses all standard SV models, including the well-known lognormal (LN) SV model. It allows to empirically compare and test all standard specifications in a very convenient way and provides a measure of the degree of departure from the classical models. A likelihood-based technique is developed for analyzing the model. Daily dollar/pound exchange rate data provide some evidence against LN model and strong evidence against all the other classical specifications. An efficient algorithm is proposed to study the economic importance of the proposed model on pricing currency options.

Highlights

  • Modelling the volatility of financial time series via stochastic volatility (SV) models has received a great deal of attention in the theoretic finance literature as well as in the empirical literature

  • For the N-SV model we report the 90% Bayesian confidence intervals for all the parameters

  • The Markov Chain Monte Carlo (MCMC) approach is developed to provide a likelihood-based inference for the analysis of proposed models

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Summary

Introduction

Modelling the volatility of financial time series via stochastic volatility (SV) models has received a great deal of attention in the theoretic finance literature as well as in the empirical literature. It has been used to price stock options in Wiggins (1987) and Scott (1987) and currency options in Chesney and Scott (1989) Since it assumes that the logarithmic volatility follows an Ornstein-Uhlenbeck (OU) process, an implication of this specification is that the marginal distribution of logarithmic volatility is normal. Other more recent classes of SV models include those proposed by Barndorff-Nielsen and Shephard (2001) and by Meddahi (2001) Despite all these alternative specifications, there is a lack of procedure for selecting an appropriate functional form of stochastic volatility.[2] The specification of the correct stochastic volatility function, on the other hand, is very important in several respects. The empirical test rejects all standard SV models and favors a nonlinear SV specification Implications of this nonlinearity on some important financial variables are examined.

A Class of Nonlinear SV Models
Why Use MCMC?
Estimating Nonlinear SV Models
Simulation Studies
Empirical Results
Implications on Option Pricing
Empirical Results for Other Exchange Rates
Conclusions and Extensions
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