| The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain & exotic options, interest rate derivatives, real options, & many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method.
In this book, PDE techniques allow the author to create a framework for modeling complex & interesting derivatives products. Having defined the PDE problem he then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics. In this book he applies the same techniques to pricing real-life derivative products. He uses both traditional (or well-known) methods as well as advanced schemes:
- Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor & multi-factor options; Early exercise features & approximation using front-fixing, penalty & variational methods; Modelling stochastic volatility models using Splitting methods; Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work; Modelling jumps using Partial Integro Differential Equations (PIDE); Free and moving boundary value problems in QF.
On the CD: Information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor & two-factor models; Source code so that you can customize the applications to suit your own needs. | |
