PDE based option pricing on GPUs

Many models used in finance end up in formulation of highly mathematical problems. Solving these equations exactly in closed form is impossible as the experience in other fields suggests. Therefore, we have to look for efficient numerical algorithms in solving complex problems such as option pricing, risk analysis, portfolio management, etc. Computational finance, generally referring to the application of computational techniques to finance, has become an integral part of modeling, analysis, and decision-making in the financial industry.

In the world of derivatives pricing there are two main working horses, namely: Monte Carlo methods and numerical PDE (Partial Differential Equation) based techniques. In the past few years, we have seen an increasing interest in the computational finance community for the application of Graphical Processing Units (GPUs). However, so far this technology has shown most promising results for Monte Carlo based approaches, while limited analysis has been done on Finite-Difference based calculations.

In this project we explore the potentials for the application of GPUs for PDE based derivatives pricing.

This project requires (at least) python, cython, numpy, scipy, nose, and cuda.

I used Canopy which included everything I needed.

$ git clone https://github.com/johntyree/fd_adi.git
$ sh autotest.sh  # builds and runs tests

Now price a test option with default parameters using the CPU, the GPU, and Monte Carlo integration.

$ python price_one_option.py -nx 150 150 -nt 150 --cpu --gpu --mc 10000 -v