Pricing passport option using higher order compact scheme

Higher order compact scheme (HOC) is used for pricing both European and American type passport option. We consider the problem for two different cases, namely, the symmetric case (which has a closed form solution) and the non-symmetric case. For the symmetric case HOC schemes result in slightly improved results as compared to the classical Crank–Nicolson implicit method, while still giving approximately second order convergence rate. In order to improve the convergence rate, grid stretching near zero accumulated wealth is introduced in the HOC schemes. The consequent higher order compact scheme with grid stretching gives better results with the rate of convergence being close to third order. For non-symmetric case we also observe similar results for both European and American type passport option. In absence of any analytic formula for the non-symmetric case, convergence rate was calculated using double-mesh differences.