Affine Models With Stochastic Market Price Of Risk

In this paper we discuss the common shortcomings of a large class of essentially-affine models in the current monetary environment of repressed rates, and we present a class of reduced-form stochastic-market-risk affine models that can overcome these problems. In particular, we look at the extension of a popular doubly-mean-reverting Vasicek model, but the idea can be applied to all essentially-affine models. The model straddles the ℙ- and ℚ-measures. By allowing for a market price of risk whose stochasticity is not fully spanned by the yield-curve state variables that enter the model specification, we break the deterministic link between the yield-curve-based return-predicting factors and the market price of risk, but we retain, on average, the observed statistical regularities reported in the literature. We discuss in detail how this approach relates to the recent work by Joslin et al. (2014) [S. Joslin, M. Priebsch & K. J. Singleton (2014) Risk premiums in dynamic term structure models with unspanned macro risk, Journal of Finance LXIX (3), 1197–1233]. We show that the parameters of the model can be estimated in a simple and robust manner using survey-like information; and that the model we propose affords a more plausible decomposition of observed market yields into expectations and risk premia during an important recent market event than the one produced by mainstream essentially-affine models.