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- Title
Option Pricing with Random Volatilities in Complete Markets.
- Authors
Eisenberg, Larry; Jarrow, Robert
- Abstract
This article presents the theory of option pricing with random volatilities in complete markets. As such, it makes two contributions. First, the newly developed martingale measure technique is used to synthesize results dating from Merlon (1973) through Eisenberg, (1985, 1987). This synthesis illustrates how Merton's formula, the CEV formula, and the Black-Scholes formula are special cases of the random volatility model derived herein. The impossibility of obtaining a self-financing trading strategy to duplicate an option in incomplete markets is demonstrated. This omission is important because option pricing models are often used for risk management, which requires the construction of synthetic options. Second, we derive a new formula, which is easy to interpret and easy to program, for pricing options given a random volatility. This formula (for a European call option) is seen to be a weighted average of Black-Scholes values, and is consistent with recent empirical studies finding evidence of mean-reversion in volatilities.
- Subjects
PRICING; MARKET volatility; FINANCIAL markets; BUSINESS finance; RISK management in business
- Publication
Review of Quantitative Finance & Accounting, 1994, Vol 4, Issue 1, p5
- ISSN
0924-865X
- Publication type
Article
- DOI
10.1007/BF01082661