The stochastic volatility model, regime switching and value-at-risk (VaR) in international equity markets

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.