TITLE:
On the Internal Consistency of the Black-Scholes Option Pricing Model
AUTHORS:
Jeremy Berkowitz
KEYWORDS:
Diffusions; Binomial Model; Arbitrage
JOURNAL NAME:
Theoretical Economics Letters,
Vol.3 No.3,
June
13,
2013
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.