On the Internal Inconsistency of the Black-Scholes Option Pricing Model

13 Pages Posted: 29 Apr 2008

See all articles by Jeremy Berkowitz

Jeremy Berkowitz

University of Houston - Department of Finance

Date Written: December 11, 2007

Abstract

We study the information structure implied by models in which the asset price is always risky and there are no arbitrage opportunities. Using the martingale representation of Harrison and Kreps (1979), a claim takes its value from the stream of discounted expected payments. Equivalently, a pricing-kernel is sufficient to value the payment stream. If a price process is always risky, then either the payment or the discount factor must also be continually risky. This observation substantially complicates the valuation of contingent claims. Many classical option pricing formulas abstract from both risky dividends and risky discount rates. In order to value contingent claims, one of the assumptions must be abandoned.

Keywords: diffusions, arbitrage

JEL Classification: G12, G13

Suggested Citation

Berkowitz, Jeremy, On the Internal Inconsistency of the Black-Scholes Option Pricing Model (December 11, 2007). Available at SSRN: https://ssrn.com/abstract=1125643 or http://dx.doi.org/10.2139/ssrn.1125643

Jeremy Berkowitz (Contact Author)

University of Houston - Department of Finance ( email )

Houston, TX 77204
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
128
Abstract Views
843
rank
276,717
PlumX Metrics