International Stochastic Discount Factors and Covariance Risk
48 Pages Posted: 23 Sep 2014 Last revised: 3 May 2019
Date Written: April 26, 2019
This research studies different dimensions of heterogeneity between countries including heterogeneities in SDF dynamics, risk premium dynamics, and the relations between SDF and risk premium dynamics. We propose a Wishart Affine Stochastic Correlation (WASC) Model for SDF dynamics. This yields quasi-closed form solutions for currency options which include Heston's stochastic volatility model as a special case of our model. We estimate the model for the US, Europe, and Japan applying the unscented Kalman Filter. Empirical results suggest that Europe and Japan are more homogeneous with respect to the US than with respect to each other. Homogeneity between SDF is higher than homogeneity with respect to Sharpe ratios. Moreover, we observe occasional breakdowns in international risk sharing. As plausibility checks we relate estimated Sharpe ratios to economic fundamentals. We find significant relations, which are in line with economic intuition. The model also fits second exchange rate moments reasonably.
Keywords: Stochastic discount factors, International model, Stochastic covariance, Stochastic risk premium, Wishart process, Currency options, Foreign exchange, Unscented Kalman filter
JEL Classification: G11, G13
Suggested Citation: Suggested Citation