Runge-Kutta-Gegenbauer relaxation for parallelised option pricing

We present an alternative approach to the classic Projected Successive Over-Relaxation (PSOR) fixed-point iterative method for pricing American options via finite-differencing. Relaxation factors for the... [ view full abstract ]

We present an alternative approach to the classic Projected Successive Over-Relaxation (PSOR) fixed-point iterative method for pricing American options via finite-differencing. Relaxation factors for the Runge--Kutta--Gegenbauer (RKG) relaxation method are prescribed via a recurrence relation derived from Gegenbauer orthogonal polynomials, thereby ensuring internal stability and rapid convergence for mixed-type systems of PDEs. The proposed method has the advantage that it does not require immediate replacement making it particularly well-suited to parallelisation of computationally intensive problems dependent on multiple assets  or factors since colouring schemes are not required. We present test results for American options under Heston's stochastic volatility model.