  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.
