Option pricing, maturity randomization and grid computing

By geometric randomization of the option maturity, we transform the n-steps backward recursion that arises in option pricing into an integral equation. The option price is then obtained solving n independent integral equations. This is accomplished by a quadrature procedure that transforms each integral equation in a linear system. Since the solution of each linear system is independent one of the other, we can exploit the potentiality of the grid architecture AGA¹. We compare different quadrature methods of the integral equation with Monte Carlo simulation. Therefore we price options (such as plain vanilla, single and double barrier options) when the underlying evolves according to different exponential Levy processes.