**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. 67, 1 (1998)

pp. 69-82

THE NUMERICAL VALUATION OF OPTIONS WITH UNDERLYING JUMPS

G. H. MEYER

**Abstract**.
A Black-Scholes type model for American options will be considered where the underlying asset price experiences Brownian motion with random jumps. The mathematical problems is an obstacle problem for a linear one-dimensional diffusion equation with a functional source term. The problem is time discretized and solved at each time level iteratively with a Riccati method. Some numerical experiments for a call and put with multiple jumps are presented. Convergence of the iteration at a given time level will be discussed for the simpler problem of a European put where there is no free boundary.

**AMS subject classification**.
65N40; Secondary 60G40

**Keywords**.

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Acta Mathematica Universitatis Comenianae

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