TITLE:
An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy
AUTHORS:
Werner Hürlimann
KEYWORDS:
State-Price Deflator, Option Pricing, Black-Scholes Model, Vasicek Model, Margrabe Formula
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.4,
March
31,
2011
ABSTRACT: We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.