Stochastic Correlation and Risk Premia in Term Structure Models

Abstract

This paper proposes and analyses a term structure model that allows for both stochastic correlation between underlying factors and an extended market price of risk specification. The issues of invariant transformation and different normalization are then considered so that a comparison between different restrictions can be made. We show that significant improvement in bond fitting is obtained by both allowing the market price of risk to have an extended affine form, and allowing the correlation between underlying factors to be stochastic as well as of variable sign. The overall model fit is more negatively impacted by the restriction on the market price of risk than the restriction of correlated factors. However, the stochastic correlation is priced significantly by market participants, though its impact on the risk premia reduces gradually as time to maturity increases. In addition, stochastic correlation is vital in obtaining good hedged portfolio positions. Certainly, the best hedged portfolio is the one that is built based on the model that takes into account both stochastic correlation and extended market price of risk.Term structure; Stochastic correlation, Risk premium; Wishart; Affine; Extended affine; Multidimensional CIR