Accelerating Convergence in Trinomial Option Pricing: Recursive Incremental Value Ordering with Repeated Richardson Extrapolation

The Black-Scholes model, widely utilized for option pricing, has evolved into a
trinomial model approach, providing an alternative means for determining option
prices. Nonetheless, the trinomial model faces limitations in terms of time efficiency
and accuracy. This study explores the acceleration of the trinomial option prices'
convergence and computation time reduction using repeated Richardson extrapolation
(RRE), achieved by recursively determining the order of incremental values.
Comparative analysis with other extrapolation methods revealed that the RRE technique
outperforms the Aitken Neville method by approximately 11%. Applied to a case study
involving technology and energy stock option pricing, this technique minimized the
required time steps to an average of 0.04 seconds, simultaneously achieving a mean
square error (MSE) value of 0.835 compared to the Black-Scholes value. Consequently,
the proposed methodology offers potential enhancements in computational efficiency
for financial applications employing nested discrete-time models.