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.
"Stephane Crepey s book starts with a few chapters on classical
stochastic processes material, ...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. Crepey 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
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