A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates

Abstract

In this paper we present a parsimonious multivariate model for exchange rate volatilities based on logarithmic high-low ranges of daily exchange rates. The multivariate stochastic volatility model decomposes the log range of each exchange rate into two independent latent factors, which could be interpreted as the underlying currency specific components. Owing to the empirical normality of the logarithmic range measure the model can be estimated conveniently with the standard Kalman filter methodology. Our results show that our model fits the exchange rate data quite well. Exchange rate news seems to be currency specific and allows identification of currency contributions to both exchange rate levels and exchange rate volatilities.Exchange rates, Multivariate stochastic volatility models, Range-based volatility,

Multivariate Stochastic Volatility: A Review

“…The quadratic expression ensures that the covariance matrices are symmetric positive definite. Tims and Mahieu (2003) proposed a range-based MSV model. As the range can be used as a measure of volatility, which is observed (or realized) when the high and low prices are recorded, Tims and Mahieu (2003) suggested a multivariate model for volatility directly, as…”

Scalable inference for a full multivariate stochastic volatility model

“…Due to both the computational complexity that increases dramatically with N and the modelling complexity produced by the necessity to stochastically evolve correlations and volatilities preserving the positive definiteness of Σ t , all existing models assume some form of model parsimony that often correspond to the simplifications suggested in the observation driven models literature. In particular, the existing multivariate stochastic volatility (MSV) models assume either constant correlations over time or some form of dynamic correlation modelling through factor models with factors being independent univariate stochastic volatility models; see, for example, Harvey et al (1994), Kim et al (1998), Pitt and Shephard (1999a), Bauwens et al (2006), Tims and Mahieu (2003).…”

Heterogeneous Asymmetric Dynamic Conditional Correlation Model with Stock Return and Range

“…In other words, these papers employ two-step estimation based on the simple CARR model. With respect to the SV class, Tims and Mahieu (2006) estimate the multivariate stochastic volatility model suggested by Harvey et al (1994), using ranges of exchange rate returns. However, the approach of Tims and Mahieu (2006) is vague for investigating such dynamic correlations.…”