International Stochastic Discount Factors and Covariance Risk

Abstract

We propose a Wishart Affine Stochastic Correlation (WASC) model for the joint dynamics of the SDF in an international economy. We derive exchange rate dynamics and a quasi-closed-form solution for currency option pricing. This solution includes Heston's stochastic volatility model as a special case. We benchmark our approach to a vector-based model inspired by Bakshi/Carr/Wu (2008, JFE). We estimate both models for the US, Europe, and Japan. Empirically, the WASC model is more robust with respect to the estimation period. In contrast to the benchmark model, estimated risk sharing indices seem to reflect the Euro crisis (2011/12) in the WASC model. Moreover, the explanatory power of filtered Sharpe ratios for stock market returns and volatilities is higher (both in- and out-of-sample).

Keywords: Stochastic discount factors, International model, Stochastic covariance, Stochastic risk premium, Wishart process, Currency options, Foreign exchange, Unscented Kalman filter

JEL Classification: G11, G13