Standard Article

Pricing Kernels

  1. Lars Peter Hansen1,
  2. Eric Renault2

Published Online: 15 MAY 2010

DOI: 10.1002/9780470061602.eqf19009

Encyclopedia of Quantitative Finance

Encyclopedia of Quantitative Finance

How to Cite

Hansen, L. P. and Renault, E. 2010. Pricing Kernels. Encyclopedia of Quantitative Finance. .

Author Information

  1. 1

    University of Chicago, Chicago, IL, USA

  2. 2

    University of North Carolina, Chapel Hill, NC, USA

Publication History

  1. Published Online: 15 MAY 2010


Pricing kernels or stochastic discount factors (SDFs) are used to represent arbitrage-free valuation operators in dynamic stochastic economies. After deriving convenient representations for prices, we provide several examples of SDFs and discuss econometric methods for estimation and testing of asset pricing models that restrict the SDFs.


  • stochastic discount factors;
  • kernels;
  • risk-neutral probabilities;
  • arbitrage;
  • incomplete markets;
  • solvency constraints;
  • limited participation;
  • econometrics;
  • generalized method of moments