Wiener Simulation

C++ Monte Carlo Methods Geometric Brownian Motion Black-Scholes Stochastic Calculus Multithreading CMake

A Monte Carlo option pricer written in C++, using the exact Geometric Brownian Motion equations and antithetic variates for variance reduction.
Simulates n possible future stock prices under GBM, then prices European call and put options by averaging discounted payoffs across all simulated paths.
Validates results against the Black-Scholes closed-form formula and reports relative error.
Able to export and plot simulated stock price paths to establish visual correctness.
Parallelised across hardware threads: paths are chunked across cores rather than spawning one thread per path, keeping thread overhead constant regardless of path count

As GBM has a closed-form solution, the pricer samples terminal prices exactly — one normal draw per path, no discretization error — rather than approximating with Euler-Maruyama steps. The Euler-Maruyama implementation is kept in the codebase as the original implementation and as a reference, since models like jump-diffusion don't have clean closed-form solutions and would need it.

Antithetic variates are used throughout: for every random draw Z, a paired path using −Z is also simulated and the two payoffs averaged before discounting. This significantly reduces variance compared to independent sampling — similar accuracy for half the number of random processes.