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Asset Pricing in Discrete Time$
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Asset Pricing in Discrete Time: A Complete Markets Approach

Ser-Huang Poon and Richard Stapleton

Print publication date: 2005

Print ISBN-13: 9780199271443

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0199271445.001.0001

Risk Aversion, Background Risk, and the Pricing Kernel

Chapter:
(p. 19 ) 2 Risk Aversion, Background Risk, and the Pricing Kernel
Source:
Asset Pricing in Discrete Time
Author(s):

Ser-Huang Poon (Contributor Webpage)

Richard Stapleton (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271445.003.0002

‘Risk Aversion, background Risk, and the Pricing Kernel’ looks in more detail at utility functions and their effect on the shape of the pricing kernel. The authors discuss the meaning of risk aversion and, in particular, ‘relative risk aversion’ and show that if relative risk aversion is constant at different levels of wealth, then the pricing kernel exhibits constant elasticity. They then show that the introduction of ‘background risk’, that is, non-hedgeable risks, causes the pricing kernel to exhibit declining elasticity. This effect on the pricing kernel is particularly significant for the pricing of options.

Keywords:   background risk, constant elasticity, declining elasticity, relative risk aversion, utility

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