Option Pricing Under Decreasing Absolute Risk Aversion

Posted: 10 Sep 1999

See all articles by Kamlesh Mathur

Kamlesh Mathur

affiliation not provided to SSRN

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance

Abstract

This article establishes bounds on option prices in an economy where the representative investor has non increasing absolute risk aversion. The bounds do not require knowledge of any specific utility parameters, nor do they require specific joint distribution assumptions between the marginal utility of aggregate consumption and the underlying stock price. To drive our results we only require that the expected marginal utility of consumption conditional on the stock price is monotone non increasing in the stock price, and that the marginal distribution of the stock price is given. With this assumption, the lower bound on option prices is given by the solution to a non-linear mathematical program. We identify the general solution of this program. If the underlying process is multinomial, we show that the lower bound is set up as if the representative investor had constant proportional risk aversion. For this case, a risk neutral valuation relationship exists. As a result, the lower bound does not depend on the drift term, nor is it affected by the number of permissible trading periods prior to expiration. Moreover, if the underlying distribution is lognormal, the lower bound is the Black Scholes price. The upper bound on option prices is also identified and its behavior as multiple portfolio opportunities exist is examined.

JEL Classification: G13

Suggested Citation

Mathur, Kamlesh and Ritchken, Peter H., Option Pricing Under Decreasing Absolute Risk Aversion. Available at SSRN: https://ssrn.com/abstract=6234

Kamlesh Mathur (Contact Author)

affiliation not provided to SSRN

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance ( email )

10900 Euclid Ave.
Cleveland, OH 44106-7235
United States
216-368-3849 (Phone)
216-368-4776 (Fax)

Register to save articles to
your library

Register

Paper statistics

Abstract Views
876
PlumX Metrics
!

Under construction: SSRN citations while be offline until July when we will launch a brand new and improved citations service, check here for more details.

For more information