We show various methods that increase the precision and convergence speed of simulated stochastic processes. We demonstrate our precision and speed by using an example from the finance world, namely that of an Asian Option. An Asian Option is a path dependent pricing mechanism that is normally priced using Monte Carlo methods, it can be thought of as a path dependent diffusion equation. We show that the precision of the simulations is increased by 70% using Control Variates (derived by approximating the true mean from an analytic closed form solution). Using sequential Monte Carlo and parallel computing across a GPU (CUDA) increases convergence speed.
Harper, Mario Y., "High Precision Rapid Convergence of Asian Options" (2014). Physics Capstone Projects. Paper 2.
Additional FilesControlVariateAsianOption2.py (2 kB)
Python Code Simple MC
bridge.r (1 kB)
R Code Brownian Bridge