A GPU accelerated hybrid lattice-grid algorithm for options pricing

Abstract

The pricing of financial derivatives is an important problem in risk analysis and real-time trading. The need for faster and more accurate pricing has led financial institutions to adopt GPU technology, but this means we need new pricing algorithms designed specifically for GPU architectures. This research tackles the design of adaptable algorithms for option evaluation using lattices, a commonly used numerical technique. Usually lattice nodes are placed on a fixed grid at a high resolution, but by coarsening the grid in areas of low error, we can reduce run-time without a reduction in accuracy. We show that this adaptable grid can be designed to map onto the underlying architecture of warp-based GPUs, providing a tradeoff between faster execution at the same error, or lower error for the same execution speed. We implemented this algorithm in platform-independent OpenCL, and evaluated it on the Nvidia Quadro K4000, across different option classes. We present accuracy and speed-up results from using our hybrid lattice mesh model over an equivalent standard lattice implementation.