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Jump-Diffusion Models for Asset Pricing in Financial ...

Birge and V. Linetsky (Eds.),Handbooks in OR & MS, Vol. 15 Copyright 2008 Elsevier All rights reservedDOI: (07)15002-7 Chapter 2 Jump-Diffusion Models for Asset Pricing inFinancial KouDepartment of Industrial Engineering and Operations Research, Columbia this survey we shall focus on the following issues related to Jump-Diffusion mod-els for Asset Pricing in Financial engineering. (1) The controversy over tailweight ofdistributions. (2) Identifying a risk-neutral Pricing measure by using the rational ex-pectations equilibrium. (3) Using Laplace transforms to Pricing options, includingEuropean call/put options, path-dependent options, such as barrier and lookback op-tions. (4) Difficulties associated with the partial integro-differential equations relatedto barrier-crossing problems. (5) Analytical approximations for finite-horizon Amer-ican options with jump risk.

Jump-Diffusion Models for Asset Pricing in Financial Engineering 77 leptokurtic and the distribution will have a higher peak and two heavier tails than those of the normal distribution.

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