Pricing derivatives on graphics processing units using Monte Carlo simulation

Abstract

International audienceThis paper is about using the existing Monte Carlo approach for pricing European and American contracts on a state-of-the-art graphics processing unit (GPU) architecture. First, we adapt on a cluster of GPUs two different suitable paradigms of parallelizing random number generators, which were developed for CPU clusters. Because in financial applications, we request results within seconds of simulation, the sufficiently large computations should be implemented on a cluster of machines. Thus, we make the European contract comparison between CPUs and GPUs using from one up to 16 nodes of a CPU/GPU cluster. We show that using GPUs for European contracts reduces the execution time by ∼ 40 and diminishes the energy consumed by ∼ 50 during the simulation. In the second set of experiments, we investigate the benefits of using GPUs' parallelization for pricing American options that require solving an optimal stopping problem and which we implement using the Longstaff and Schwartz regression method. The speedup result obtained for American options varies between two and 10 according to the number of generated paths, the dimensions, and the time discretization

Dual Pricing of American Options by Wiener Chaos Expansion

“…These techniques are known to suffer from the curse of dimensionality: global regression methods lead to high dimensional linear algebra problems, whereas local methods see the number of domains blow up with the dimension. Despite the numerous parallel implementation of this techniques (see for instance Dung Doan et al [2010], Abbas-Turki et al [2014]), we cannot expect to obtain a fully scalable algorithm. In this work, we follow the dual approach initiated by Rogers [2002] and Haugh and Kogan [2004], which can naturally handle path dependent options.…”

Toward a coherent Monte Carlo simulation of CVA

“…The parallel suitability of Monte Carlo allows to increase the accuracy using more computing resources including many-cores architectures as done in [1]. Nevertheless, the complexity of square Monte Carlo remains too high.…”

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An OpenCL implementation of a forward sampling algorithm for CP-logic

“…This fits in a natural way into the GPGPU paradigm, where a massive number of weak processors can each compute a single sample. Indeed, in the literature, we already find many examples of GPGPU sampling methods, e.g., in the context of computer graphics [22] or financial simulations [1]. However, to the best of our knowledge, this paper is the first to apply GPGPU sampling to PLP query answering.…”