Advanced Stochastic Monte Carlo Optimization Methods for Two-Dimensional European Style Options

Multidimensional option pricing poses significant challenges and is a fundamental area in large-scale finance. A European call option grants the holder the right to buy a specific quantity of an underlying asset (S) at a predetermined price (E) and time (T), without the obligation to do so. Monte Carlo and quasi-Monte Carlo methods are powerful tools for solving various financial problems. This paper addresses the challenge of determining the fair value of two and higher dimensional European style options. Monte Carlo methods are particularly effective and useful, especially in higher dimensions, for option pricing problems. This paper proposes simulation optimization methods that employ both low discrepancy sequences and variance reduction techniques to enhance the accuracy of standard approaches for European style options. Improving accuracy is critical for more reliable European option pricing results. Additionally, this approach can be used in situations where other deterministic methods fail, such as high dimensions, complex contract specifications, and other challenging scenarios.