Option Pricing: A New MCGP Approach

Pricing American-style options remains a challenging problem in computational finance due to the presence of early-exercise features and the absence of closed-form valuation formulas. Among simulation-based methods, the Least Squares Monte Carlo (LSMC) approach has become one of the most widely adopted techniques for approximating continuation values in optimal stopping problems. However, the accuracy of LSMC is highly dependent on the specification of predefined regression basis functions, which may introduce approximation bias when continuation-value dynamics exhibit strong nonlinearities. This paper proposes a Monte Carlo--Genetic Programming (MCGP) framework for American option pricing. The proposed methodology combines Monte Carlo simulation for generating risk-neutral asset-price trajectories with Genetic Programming-based symbolic regression for adaptive continuation-value estimation. Unlike conventional LSMC implementations, the proposed framework does not rely on predefined polynomial basis functions. Instead, continuation-value functions are evolved directly from simulated data through an evolutionary symbolic-learning process, enabling greater structural flexibility and potentially reducing projection bias associated with a restricted predefined basis. Numerical experiments conducted under different volatility and interest-rate regimes yield lower descriptive MAE and RMSE point estimates for MCGP than for the conventional LSMC benchmark. A controlled cross-family benchmark additionally compares MCGP with cubic-basis LSMC, neural-network continuation regression, and Gaussian kernel ridge regression on common Monte Carlo paths. In the resulting 10-replication benchmark, MCGP has the lowest descriptive MAE and RMSE at both 20\% and 40\% volatility, although paired comparisons with LSMC and the neural benchmark are not statistically significant in this small sample. A separate 50-replication matched MCGP--LSMC diagnostic likewise does not reject equality of absolute-error performance at the 5\% level. The results therefore support adaptive symbolic regression as an interpretable and competitively accurate alternative rather than establishing universal statistical superiority. A controlled runtime diagnostic additionally confirms that the evolutionary search is substantially more computationally expensive than the small-basis LSMC regression in the present reproducible implementation; MCGP is therefore not claimed to provide a general speed advantage.