26. Modern Monte Carlo Methods and GPU Computing

Pricing early-exercise options under multi-dimensional stochastic processes is a major challenge in the financial sector. In Leitao and Oosterlee (Int J Comput Math 92(12):2433–2454, 2015), a parallel GPU version of the Monte Carlo based Stochastic Grid Bundling Method (SGBM) (Jain and Oosterlee, Appl Math Comput 269:412–431, 2015) for pricing multi-dimensional Bermudan options is presented. The method is based on a combination of simulation, dynamic programming, regression and bundling of Monte Carlo paths. To extend the method’s applicability, the problem dimensionality and the number of bundles is increased drastically. This makes SGBM very expensive in terms of computational costs on conventional hardware systems. A parallelization strategy of the method is developed and the GPGPU paradigm is used to reduce the execution time. An improved technique for bundling asset paths, which is more efficient on parallel hardware, is introduced. Thanks to the performance of the GPU version of SGBM, we can fully exploit the method and deal with very high-dimensional problems. Pricing results and comparisons between sequential and GPU parallel versions are presented.