Monte Carlo methods for pricing financial options

Pricing financial options is amongst the most important and challenging problems in the modern financial industry. Except in the simplest cases, the prices of options do not have a simple closed form solution and efficient computational methods are needed to determine them. Monte Carlo methods have increasingly become a popular computational tool to price complex financial options, especially when the underlying space of assets has a large dimensionality, as the performance of other numerical methods typically suffer from the ‘curse of dimensionality’. However, even Monte-Carlo techniques can be quite slow as the problem-size increases, motivating research in variance reduction techniques to increase the efficiency of the simulations. In this paper, we review some of the popular variance reduction techniques and their application to pricing options. We particularly focus on the recent Monte-Carlo techniques proposed to tackle the difficult problem of pricing American options. These include: regression-based methods, random tree methods and stochastic mesh methods. Further, we show how importance sampling, a popular variance reduction technique, may be combined with these methods to enhance their effectiveness. We also briefly review the evolving options market in India.