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



This study proposes an approximation method for pricing barrier options and lookback options with continuous monitoring. 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 an approximation formula. Two features of this method are that it is straightforward and easily implementable. Nevertheless, the approximation prices generated by the method are quite accurate and the calculation speed is remarkably fast, regardless of the type of option and time to maturity.