Numerical techniques play a crucial role in the derivative pricing of options, particularly when no closed-form analytical formula exists. This study aims to compare two prominent numerical methods: Monte Carlo simulation and finite difference methods, as they are applied to the hybrid Heston-SABR model. The hybrid Heston SABR model, provides a sophisticated basis for modeling the dynamics of financial derivatives. In this paper, we explore these two primary numerical methods commonly employed by financial experts to determine option prices. We evaluate the performance, accuracy, and computational efficiency of Monte Carlo simulation and finite difference methods in solving the partial differential equations (PDEs) and pricing options under the stated model. We assess the convergence of both methods for valuing European options within the hybrid Heston-SABR framework. We observed that when pricing European options under this model, both approaches converge faster, are more accurate, and are unconditionally stable. We have also established that the numerical method's accuracy and stability are affected by the maturity time. Further, we have determined that changing the maturity time T affects the trade-off between numerical accuracy and computing efficiency in pricing European call options for the two numerical approaches under this hybrid model.

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