Robust Numerical Approach to CRR Model under Self-financing Assumption - Abonongo, John; Chidzalo, Patrick (Statistics, Optimization & Information Computing, 2025)
The accurate pricing of options is crucial for minimizing financial risks and making informed investment decisions in dynamic markets. Traditional models like the Black-Scholes often fail to account for the early exercise feature of American options and the self-financing replicating portfolio concept, leading to less realistic pricing. This study address these gaps by employing various metaheuristic algorithms, including Particle Swarm Optimization, Differential Evolution, Grey Wolf Optimization, and Simulated Annealing Algorithm, to estimate the parameters for a modified Cox-Ross-Rubinstein model. We derive a Brownian motion model incorporating upward and downward factors and use the Euler-Maruyama method to simulate stock price paths. By comparing these simulated paths with real stock data, we evaluate the effectiveness of the estimated parameters. Additionally, we improve the numerical method for estimating American option prices via the CRR model by integrating the self-financing replicating portfolio concept. The results demonstrate that Particle Swarm and Grey Wolf optimization algorithms provide parameter estimates that yield simulated paths closely matching the real stock data, thereby offering computationally realistic prices for American options. This study highlights the potential of integrating metaheuristic algorithms with traditional models to enhance the accuracy and reliability of option pricing.