The Stochastic Volatility Model, Regime Switching and Value-at-Risk (VaR) in International Equity Markets

Ata Assaf

doi:10.4236/jmf.2017.72026

Abstract

In this paper, we estimate two stochastic volatility models applied to international equity markets. The two models are the log-normal stochastic volatility (SV) model and the two-regime switching model. Then based on the one-day-ahead forecasted volatility from each model, we calculate the Value-at-Risk (VaR) in each market. The estimated VaR measures from the SV are higher than those obtained from the regime-switching model for all markets and over all horizons. The exception is the Japanese market, where the stochastic volatility model generates low VaR estimates. Comparing those estimates with the unconditional return distribution, the two models generate smaller VaR measures; an evidence of the two models capturing volatility changes in international equity markets. Finally, we backtest each model and find that the performance of both models is the worst for the Canadian stock market, while the regime switching model does poorly for Germany. The results have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives.

Highlights

Volatility is a key ingredient for derivative pricing, portfolio optimization and value-at-risk analysis
Comparing how the Value-at-Risk behaves with the time horizon, value at risk measures increase more slowly with horizon under the regime switching model than those obtained under the stochastic volatility model4. The performance of both models are backtested using conditional and unconditional tests and we find that the Canadian equity market represented by the S & P/TSX performs the worst among all markets, while the DAX seems to be better modeled by the stochastic volatility model as opposed to that of the regime switching model
A variety of estimation procedures has been proposed for the stochastic volatility models, including for example the Generalized Method of Moments (GMM) used by Melino and Turnbull [35], the Quasi Maximum Likelihood (QML) approach followed by Harvey et al [36] and Ruiz [37], the Efficient Method of Moments (EMM) applied by Gallant et al [38], and Markov-Chain Monte Carlo (MCMC) procedures used by Jacquier et al [39] and Kim et al [40]

Summary

Introduction

Volatility is a key ingredient for derivative pricing, portfolio optimization and value-at-risk analysis. For surveys on the extensive GARCH literature we refer to Bollerslev et al [5], Bera and Higgins [6] and Bollerslev et al [7] and for stochastic volatility we refer to Taylor [8], Ghysels et al [9] Shephard [10], and Broto and Ruiz [11] Both models are defined by their first and second moments. The first one is their solid theoretical background, as they can be interpreted as discretized versions of stochastic volatility continuous-time models put forward by modern finance theory (see Hull and White [12]) The second is their ability to generalize from univariate to multivariate series, as far as their estimation and interpretation are concerned. A number of econometric methods have been proposed to solve the problem of estimation of stochastic volatility models

Methods

Results

Conclusion