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Numerical Solution of Jump-Diffusion SDEs

by Kay Giesecke of Stanford University, and
Gerald Teng of Stanford University

August 1, 2013

Abstract: This paper develops, analyzes and tests a discretization scheme for jump-diffusion processes with general state-dependent drift, volatility, jump intensity, and jump size. The scheme allows for an unbounded jump intensity, a feature of many standard jump-diffusion models in finance, economics, and other disciplines. It constructs the jump times as time-changed Poisson arrival times, and generates the process between the jump epochs using Euler discretization. Under technical conditions on the coefficient functions of the jump-diffusion, the convergence of the discretization error is proved to be of weak order one. The use of higher-order methods between jumps does generally not improve the weak order of convergence. Extensions to point processes driven by jump-diffusions are provided. Numerical experiments illustrate the results.

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