Approximation Method Using Black-Scholes Formula for Barrier Option Pricing under Lévy Models

Abstract

This study proposes an approximation method for pricing continuously monitored barrier options. We employ a class of Lévy processes as the driving factor of an underlying stock price and consider a mimicking process for approximation. Randomizing the Black-Scholes formula associated with the mimicking process leads to a primary approximation formula. We then develop a probability matching adjustment for improving the accuracy of the primary approximation formula. This method is straightforward and easily implementable. Nevertheless, the approximation prices are reasonably accurate, and the calculation speed is remarkably fast, regardless of time to maturity.