First and second generation lookback and barrier options: enhancing pricing accuracy through Conditional Monte Carlo

Abstract

This paper addresses the challenges associated with pricing exotic options, specifically path-dependent ones, with a focus on the limitations of standard Monte Carlo simulations and the advantages provided by Conditional Monte Carlo methods, introduced by Babsiri and Noel in 1998. Path dependent options, such as first and second-generation barrier and lookback options, require continuous monitoring of asset prices throughout their lifetime, making accurate pricing computationally demanding and prone to errors when using traditional Monte Carlo methods. This work begins by presenting different exotic options, offering a detailed comparison between the exact pricing formulas and the results obtained from Crude Monte Carlo simulations. The Conditional Monte Carlo method is then applied to address the bias introduced by discrete monitoring intervals in the simulations, a critical issue in path-dependent options. A market case based on the valuation of a Bonus Cap certificate has also been shown.