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Pricing Derivatives Under Levy Models - Modern Finite-Difference and Pseudo-Differential Operators Approach (Paperback, 1st ed. 2017)
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Pricing Derivatives Under Levy Models - Modern Finite-Difference and Pseudo-Differential Operators Approach (Paperback, 1st ed. 2017)
Series: Pseudo-Differential Operators, 12
Expected to ship within 10 - 15 working days
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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 Levy 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 Levy
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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