Why are Options Expensive?

38 Pages Posted: 11 Nov 2008  

Marti G. Subrahmanyam

New York University - Stern School of Business

Günter Franke

affiliation not provided to SSRN

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance

Date Written: February 1998

Abstract

Many valuation models in financial economics are developed using the pricing kernel approach to adjust for risk through the equivalent martingale representation. Often it is assumed, explicitly or implicitly, that the pricing kernel exhibits constant elasticity with respect to the price of the market portfolio. In a representative agent economy this would be close to assuming that the representative agent has constant proportional risk aversion. The elasticity of the pricing kernel has also implications for the pricing of options. This paper shows, first, that given the forward price of the market portfolio, all European options would have higher prices if the elasticity of the pricing kernel was declining instead of constant. Moreover, a volatility smile-effect is generated. Second, the paper shows that the standard geometric Brownian motion underlying the Black/Scholes model requires constant elasticity of the pricing kernel . Third, if the price of the market portfolio at the expiration date of an option is lognormally distributed, then declining elasticity of the pricing kernel implies a stochastic process which is characterized by higher volatility and negative autocorrelation. Thus, declining elasticity of the pricing kernel can explain several empirical findings.

Suggested Citation

Subrahmanyam, Marti G. and Franke, Günter and Stapleton, Richard C., Why are Options Expensive? (February 1998). NYU Working Paper No. FIN-98-065. Available at SSRN: https://ssrn.com/abstract=1297801

Marti G. Subrahmanyam (Contact Author)

New York University - Stern School of Business ( email )

Stern School of Business,
44 West 4th Street, Suite 9-68
New York, NY 10012-1126
United States
212-998-0348 (Phone)
212-995-4233 (Fax)

Günter Franke

affiliation not provided to SSRN

No Address Available

Richard C. Stapleton

University of Strathclyde - Department of Accounting and Finance ( email )

Curran Building
100 Cathedral Street
Glasgow G4 0LN
United Kingdom
+44 1524 381 172 (Phone)
+44 1524 846874 (Fax)

Paper statistics

Downloads
34
Abstract Views
542