A method of moments approach to pricing double barrier contracts driven by a general class of jump diffusions

TL;DR

This paper introduces a method of moments approach for pricing barrier options under jump diffusion models, providing tight bounds and efficient computation compared to Monte Carlo methods.

Contribution

It develops a novel method of moments framework for barrier option pricing under general jump diffusion models, with proven convergence and practical numerical bounds.

Findings

Tight bounds achieved with short computation times

Method applicable to various barrier options and models

Numerical results compare favorably with Monte Carlo simulations

Abstract

We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear programming problems. Subsequently approximating those systems by finite dimensional linear programming problems, upper and lower bounds for the prices of such options are found. As numerical illustration we apply the method to the valuation of several barrier-type options (double barrier knockout option, American corridor and double no touch) under a number of different models, including a case with deterministic interest rates, and compare with Monte Carlo simulation results. In all cases we find tight bounds with short execution times. Theoretical convergence results are also provided.