Monte Carlo methods

With rising complexity and diversity of upcoming derivative securities, analytically tractable or closed-form pricing methods are difficult to find or sometimes even inexistent. Monte Carlo simulation represents a powerful and flexible alternative pricing method. The goal of this book is to discuss and implement the fundamentals of Monte Carlo methods and to introduce the wide use of this approach in finance, especially in pricing interest rate derivatives. The book provides an extensive treatment of the entire Monte Carlo simulation theory and is roughly divided into three parts. The first part focuses on random number generation and on increasing efficiency methods for Monte Carlo, such as variance reduction techniques or low-discrepancy sequences. In the following part different term structure models are developed and the link to the simulation theory is established. In the third and final part ordinary and extended Monte Carlo algorithms are implemented and corresponding simulations are run in order to analyze Bermudan swaption prices in detail. The target audience of this book is finance graduate students or professionals with similar background and interests.