Numerical Solution of Jump-Diffusion SDEs by Kay Giesecke (Stanford)

Event Date: 

Monday, November 27, 2017 -
3:30pm to 4:30pm

Title: Numerical Solution of Jump-Diffusion SDEs

Abstract: Jump-diffusion processes are widely used in finance and economics. They serve as models for asset, commodity and energy prices, interest and exchange rates, and the timing of corporate and sovereign defaults. The distributions of jump-diffusions are rarely analytically tractable, so Monte Carlo simulation methods are often used to treat the pricing, risk management, and statistical estimation problems arising in applications of jump-diffusion models. This paper formulates and analyzes a discretization scheme for a multi-dimensional jump-diffusion process with general state-dependent drift, volatility, jump intensity, and jump size. The jump times of the process are constructed as time-changed Poisson arrival times, and the Euler method is used to generate the process between the jump epochs. Under conditions on the coefficient functions specifying the process, the scheme is proved to converge weakly with order one for functions with polynomial growth. The use of higher-order methods between the jumps does generally not improve the weak order of convergence. Numerical experiments illustrate the results. This is joint work with A. Shkolnik, G. Teng, Y. Wei.