A simple example of a Monte Carlo solution to a problem is for calculating. Monte Carlo approaches were introduced by Ulam and von Neumann in the 1940s with the aim of simulating nuclear reactions (Metropolis 1987). Overall, we find that a single GeForce 8 GPU generates Gaussian random numbers 26 times faster than a Quad Opteron 2.2 GHz CPU, and we find corresponding speedups of 59x and 23x in the two financial examples. We then demonstrate how these random number generators can be used in real simulations, using two examples of valuing exotic options using CUDA. We describe two methods for generating Gaussian random numbers, one of which works by transforming uniformly distributed numbers using the Box-Muller method, and another that generates Gaussian distributed random numbers directly using the Wallace method. In this chapter, we discuss methods for generating random numbers using CUDA, with particular regard to generation of Gaussian random numbers, a key component of many financial simulations. 2006 has investigated random number generation in older generations of GPUs, but the latest generation of completely programmable GPUs has different characteristics, requiring a new approach. There is an extensive body of literature devoted to random number generation in CPUs, but the most efficient of these make fundamental assumptions about processor architecture and performance: they are often not appropriate for use in GPUs. These generators must meet the conflicting goals of being extremely fast while also providing random number streams that are indistinguishable from a true random number source. However, a key component within Monte Carlo simulations is the random number generators (RNGs) that provide the independent stochastic input to each trial. The independent trials are inherently parallelizable, and they typically consist of dense numeric operations, so GPUs provide an almost ideal platform for Monte Carlo simulations. The results of the independent trials are then combined to extract the average answer, relying on the Law of Large Numbers, which states that as more trials are combined, the average answer will converge on the true answer. The defining characteristic of Monte Carlo simulations is the use of multiple independent trials, each driven by some stochastic (random) process. Monte Carlo methods provide approximate numerical solutions to problems that would be difficult or impossible to solve exactly. Efficient Random Number Generation and Application Using CUDA You can also subscribe to our Developer News Feed to get notifications of new material on the site.Ĭhapter 37. The CD content, including demos and content, is available on the web and for download.
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