An Options Pricing Formula with Volume as a Variable

Abstract

I study jump stochastic processes for stock price movements. I show that if the jumps are identically distributed random variables independent of the times of the jumps, then as the Poisson parameter tends to infinity, the stock price process becomes geometric Brownian motion. I derive a {\it no-arbitrage} options pricing formula for European options based on a theoretical tool called {\it almost replicability} of contingent claims. The model is compared with the Black-Scholes formula for a wide variety of call options, and pricing biases of Black-Scholes (versus this model) are summarized.

JEL Classification: G13