EAN: 9781493967902

PRICING DERIVATIVES UNDER LÉVY MODELS - ANDREY ...

This monograph presents a novel numerical approach to solving partial integro-differential
equations arising in asset pricing models with jumps  which greatly exceeds the efficiency of
existing approaches. The method  based on pseudo-differential operators and several original
contributions to the theory of finite-difference schemes  is new as applied to the Lévy
processes in finance  and is herein presented for the first time in a single volume. The
results within  developed in a series of research papers  are collected and arranged together
with the necessary background material from Lévy processes  the modern theory of
finite-difference schemes  the theory of M-matrices and EM-matrices  etc.  thus forming a
self-contained work that gives the reader a smooth introduction to the subject. For readers
with no knowledge of finance  a short explanation of the main financial terms and notions used
in the book is given in the glossary. The latter part of the book demonstrates the efficacy of
the method by solving some typical problems encountered in computational finance  including
structural default models with jumps  and local stochastic volatility models with stochastic
interest rates and jumps. The author also adds extra complexity to the traditional statements
of these problems by taking into account jumps in each stochastic component while all jumps are
fully correlated  and shows how this setting can be efficiently addressed within the framework
of the new method. Written for non-mathematicians  this book will appeal to financial engineers
and analysts  econophysicists  and researchers in applied numerical analysis. It can also be
used as an advance course on modern finite-difference methods or computational finance.

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