Backward stochastic differential equations (BSDEs) provide a general
mathematical framework for solving pricing and risk management questions
of financial derivatives. They are of growing importance for nonlinear
pricing problems such as CVA computations that have been developed since
the crisis. Although BSDEs are well known to academics, they are less
familiar to practitioners in the financial industry. In order to fill
this gap, this book revisits financial modeling and computational
finance from a BSDE perspective, presenting a unified view of the
pricing and hedging theory across all asset classes. It also contains a
review of quantitative finance tools, including Fourier techniques,
Monte Carlo methods, finite differences and model calibration schemes.
With a view to use in graduate courses in computational finance and
financial modeling, corrected problem sets and Matlab sheets have been
provided.
Stéphane Crépey's book starts with a few chapters on classical
stochastic processes material, and then... fasten your seatbelt... the
author starts traveling backwards in time through backward stochastic
differential equations (BSDEs). This does not mean that one has to read
the book backwards, like a manga! Rather, the possibility to move
backwards in time, even if from a variety of final scenarios following a
probability law, opens a multitude of possibilities for all those
pricing problems whose solution is not a straightforward expectation.
For example, this allows for framing problems like pricing with credit
and funding costs in a rigorous mathematical setup. *This is, as far as
I know, the first book written for several levels of audiences, with
applications to financial modeling and using BSDEs as one of the main
tools, and as the song says: "it's never as good as the first time".
*
Damiano Brigo, Chair of Mathematical Finance, Imperial College London
While the classical theory of arbitrage free pricing has matured, and
is now well understood and used by the finance industry, the theory of
BSDEs continues to enjoy a rapid growth and remains a domain restricted
to academic researchers and a handful of practitioners. Crépey's book
presents this novel approach to a wider community of researchers
involved in mathematical modeling in finance. It is clearly an essential
reference for anyone interested in the latest developments in
financial mathematics.
Marek Musiela, Deputy Director of the Oxford-Man Institute of
Quantitative Finance
