Market Price of Risk Specifications for Affine Models: Theory and Evidence

39 Pages Posted: 5 Apr 2004

See all articles by Patrick Cheridito

Patrick Cheridito

ETH Zurich

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Robert L. Kimmel


Date Written: December 11, 2003


We extend the standard specification of the market price of risk for affine yield models of the term structure of interest rates, and estimate several models using the extended specification. For most models, the extended specification fits US data better than standard specifications, often with extremely high statistical significance. Our specification yields models that are affine under both objective and risk neutral probability measures, but is never used in financial applications, probably because of the difficulty of applying traditional methods for proving the absence of arbitrage. Using an alternate method, we show that the extended specification does not permit arbitrage opportunities, provided that under both measures the state variables cannot achieve their boundary values. Likelihood ratio tests show our extension is statistically significant for four of the models considered at the conventional 95% confidence level, and at far higher levels for three of the models. The results are particularly strong for affine diffusions with multiple square-root type variables. Although we focus on affine yield models, our extended market price of risk specification also applies to any model in which Feller's square-root process or a multivariate extension is used to model asset prices.

Keywords: Affine, Girsanov, arbitrage, Feller

JEL Classification: C13, C51, G12

Suggested Citation

Cheridito, Patrick and Filipovic, Damir and Kimmel, Robert L., Market Price of Risk Specifications for Affine Models: Theory and Evidence (December 11, 2003). Available at SSRN: or

Patrick Cheridito

ETH Zurich ( email )

Department of Mathematics
8092 Zurich

Damir Filipovic

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Lausanne, 1015


Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Robert L. Kimmel (Contact Author)


No Address Available

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics