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 BlackScholes
equation in the 1970's we have seen a surge in the number of models for
a wide range of products such as plain and exotic options, interest rate
derivatives, real options and 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 we employ partial differential equations
(PDE) to describe a range of onefactor and multifactor derivatives
products such as plain European and American options, multiasset
options, Asian options, interest rate options and real options. PDE
techniques allow us to create a framework for modeling complex and
interesting derivatives products. Having defined the PDE problem we 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, to name just a few.
In this book we apply the same techniques to pricing reallife
derivative products. We use both traditional (or wellknown) methods as
well as a number of advanced schemes that are making their way into the
QF literature:
 CrankNicolson, exponentially fitted and
higherorder schemes for onefactor and multifactor options
 Early exercise features and approximation using
frontfixing, penalty and variational methods
 Modelling stochastic volatility models using
Splitting methods
 Critique of ADI and CrankNicolson 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
Included with the book is a CD containing information
on how to set up FDM algorithms, how to map these algorithms to C++ as
well as several working programs for onefactor and twofactor models.
We also provide source code so that you can customize the applications
to suit your own needs.
Finite Difference methods in Financial Enginering
by Daniel Duffy
Wiley
ISBN: 9780470858820
