Advanced Monte Carlo methods for pricing Bermudan options and their applications in real options analysis

Pricing options with early exercise features is a challenging problem in mathematical finance. There is no general closed-form solutions available. We have implemented three established Monte Carlo methods in R for pricing Bermudan options: the random tree method, the stochastic mesh method and the least-squares Monte Carlo method (LSMC). We have also adopted the expectation-maximization (EM) control algorithm recently pro- posed in the literature and adapted this method for pricing Bermudan options. The numerical analyses find LSMC has the best performance; and have been extended to the improvements on LSMC via considering regression schemes such as piecewise linear regression and smoothing splines, random number generating process using low-discrepancy sequences and the usage of European options as control variates. The algorithm has also been applied to study a standard real option problem, the option to delay an investment project. The implemented algorithm is a powerful tool to solve many important application problems of decision under uncertainty in realistic settings that can be considered in further research.