High Precision Rapid Convergence of Asian Options

Mario Harper

Document Type

Presentation

Journal/Book Title/Conference

USU Student Showcase

Publication Date

4-2014

Faculty Mentor

Tyler Brough

Abstract

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.

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