By Andrey Itkin
This monograph provides a unique numerical method of fixing partial integro-differential equations coming up in asset pricing types with jumps, which drastically exceeds the potency of latest techniques. the tactic, in response to pseudo-differential operators and a number of other unique contributions to the idea of finite-difference schemes, is new as utilized to the Lévy strategies in finance, and is herein provided for the 1st time in one quantity. the implications inside of, constructed in a chain of analysis papers, are accumulated and organized including the mandatory historical past fabric from Lévy techniques, the trendy conception of finite-difference schemes, the idea of M-matrices and EM-matrices, etc., therefore forming a self-contained paintings that provides the reader a tender advent to the topic. For readers without wisdom of finance, a brief clarification of the most monetary phrases and notions utilized in the publication is given within the glossary.
The latter a part of the publication demonstrates the efficacy of the strategy by way of fixing a few regular difficulties encountered in computational finance, together with structural default versions with jumps, and native stochastic volatility types with stochastic rates of interest and jumps. the writer additionally provides additional complexity to the conventional statements of those difficulties by means of making an allowance for jumps in every one stochastic part whereas all jumps are absolutely correlated, and exhibits how this atmosphere could be successfully addressed in the framework of the recent method.
Written for non-mathematicians, this e-book will attract monetary engineers and analysts, econophysicists, and researchers in utilized numerical research. it will probably even be used as an advance direction on smooth finite-difference equipment or computational finance.
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Pricing Derivatives Under Lévy Models: Modern Finite-Difference and Pseudo-Differential Operators Approach by Andrey Itkin