On the Internal Inconsistency of the Black-Scholes Option Pricing Model
13 Pages Posted: 29 Apr 2008
Date Written: December 11, 2007
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: Suggested Citation