Option Pricing with Random Risk Aversion

22 Pages Posted: 28 Nov 2020

See all articles by Luiz Vitiello

Luiz Vitiello

University of Essex - Essex Business School

Ser-Huang Poon

Alliance Manchester Business School, University of Manchester; Alan Turing Institute

Date Written: October 14, 2020

Abstract

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent and aggregate wealth and the underlying asset have a bi-variate transformed-normal distribution. Our results show that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. Also, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Finally, an empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

Keywords: State-Dependent Risk Aversion, Random Risk Aversion, Non-Monotonic Pricing Kernel, Transformed Normal Distribution

JEL Classification: G12, G13, G22

Suggested Citation

Vitiello, Luiz and Poon, Ser-Huang, Option Pricing with Random Risk Aversion (October 14, 2020). Available at SSRN: https://ssrn.com/abstract=3711386 or http://dx.doi.org/10.2139/ssrn.3711386

Luiz Vitiello (Contact Author)

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

Ser-Huang Poon

Alliance Manchester Business School, University of Manchester ( email )

Alliance Manchester Business School
Booth Street West
Manchester, Manchester M15 6PB
United Kingdom
+44 161 275 4031 (Phone)
+44 161 275 4023 (Fax)

HOME PAGE: http://www.manchester.ac.uk/research/Ser-huang.poon/

Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

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