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Journal of Financial Econometrics Advance Access originally published online on April 15, 2009
Journal of Financial Econometrics 2009 7(3):199-246; doi:10.1093/jjfinec/nbp004
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Inference on Risk-Neutral Measures for Incomplete Markets

Hiroaki Kaido
     University of California, San Diego

Halbert White
     University of California, San Diego

Address correspondence to Halbert White, Department of Economics, University of California, San Diego, CA 92093-0508, USA, or e-mail: drhalwhite{at}yahoo.com.

JEL Classification: C12, C13, G12


  Abstract

This paper proposes an econometric framework to estimate market risk prices associated with risk-neutral measures Q under incomplete markets. We show that, under incomplete markets, the market price of risk is not point-identified but is instead identified as a bounded subset of an affine subspace. On the other hand, a structural assumption fully identifies diffusion coefficients for the data-generating probability measure P. We apply Kaido and White's (2008, Discussion Paper, University of California, San Diego) two-stage extension of Chernozhukov, Hong, and Tamer's (2007, Econometrica, 75(5), 1243–1284) partial identification framework to construct a set estimator and confidence regions for the identified set of market risk prices and to test hypotheses. We apply our results to study international risk sharing and risk premiums for market cap range indexes.

KEYWORDS: incomplete markets, partial identification, risk-neutral measure, set estimation

We thank the editor and two anonymous referees, Yacine Aït-Sahalia, Caio Almeida, Peter Carr, Richard Carson, Graham Elliott, Stephen Figlewski, Wolfgang Härdle, Mark Henry, Han Hong, Ivana Komunjer, Nour Meddahi, Andres Santos, Ross Starr, Yixiao Sun, Allan Timmermann, Rossen Valkanov, Ruth Williams, seminar participants at UCSD's GSRS, Econometrics reading group, Rady School of Management, and participants at the 2008 SoFiE Conference for their helpful comments and suggestions. Kaido gratefully acknowledges financial support from the Nakajima Foundation.

Received August 21, 2008; revised March 12, 2009; accepted March 13, 2009


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