PRICING AMERICAN OPTIONS WITH THE RUNGE–KUTTA–LEGENDRE FINITE DIFFERENCE SCHEME

This paper presents the Runge–Kutta–Legendre (RKL) finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of stability region, comparatively to Runge–Kutta–Chebyshev scheme follows. We then explore problem pricing American options with RKL under one factor Black–Scholes and two Heston stochastic volatility models, as well butterfly spread digital uncertain model, where a Hamilton–Jacobi–Bellman partial differential equation needs be solved. order convergence these problems, option greeks stability, compared literature popular schemes such Crank–Nicolson, Rannacher time-stepping.