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Title: Multi-Asset Option Pricing with Levy Process
Keywords: Levy Process, PIDE, Finite Element Method, Jump Diff usion, Black-Scholes Equation, Multi-Asset Options
Issue Date: 9-Sep-2009
Source: ZHOU JINGHUI (2009-09-09). Multi-Asset Option Pricing with Levy Process. ScholarBank@NUS Repository.
Abstract: The motivation of this dissertation is to present a fi nite element method for a partial integro-di fferential equation (PIDE) to price multi-asset options with underlying price processes modeled as an exponential Levy process. In the dissertation we provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-based solution. Then we discuss the localization of the in finite domain problem to a finite domain, and an explicit-implicit time-discretization of the PIDE in the domain, where the space-discretization is done through a standard continuous finite element method, and provide a localization error estimate from in finite domain to finite domain and a discretization error estimate for the numerical solution of the localized problem where two assets are assumed to have uncorrelated jumps. Based on the explicit-implicit finite element method, we can solve the PIDE numerically for European options and barrier options on two risky assets. The analytic solution for a polynomial option with payoff $H(S1; S2) = S_1^p S_2^q$ under jump di ffusion model is derived for the purpose of numerical experiment. Numerical experiments for Merton's normal jump di ffusion model, Kou's double exponential jump di ffusion model are performed with smooth and nonsmooth initial conditions.
Appears in Collections:Ph.D Theses (Open)

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