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On the Internal Consistency of the Black-Scholes Option Pricing Model
Department of Finance, Bauer College of Business, University of Houston, Houston, USA
- 1 Department of Finance, Bauer College of Business, University of Houston, Houston, USA
Theoretical Economics Letters·Volume 03 (2013)·Pages 191–195·Published 7 June 2013·DOI10.4236/tel.2013.33032
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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 [1], 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.
KeywordsDiffusionsBinomial ModelArbitrage
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