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Monte Carlo on GPUs

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Monte Carlo simulation is well-suited for GPU acceleration due to its highly parallel nature. GPUs provide lower cost and higher performance than CPUs for Monte Carlo applications. Numerical libraries for GPUs allow developers to focus on their models rather than reimplementing basic components. NAG has developed GPU libraries including random number generators and is working with financial institutions to apply Monte Carlo simulations to problems in finance.

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Monte Carlo Simulation and its Efficient Implementation Robert Tong ,[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object]
Why use Monte Carlo methods? ,[object Object],[object Object],[object Object],[object Object],[object Object]
The elements of Monte Carlo simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],The demand for ever increasing performance
Ways to improve performance in Monte Carlo simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Higher order methods – 1 (work by Kai Zhang, University of Warwick, UK)
Higher order methods – 2
Numerical example – 1
Numerical example – 1a
Numerical example – 1b
Numerical example – 2a
Numerical example – 2b
GPU acceleration ,[object Object],[object Object]
The Emergence of GPGPU Computing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Current GPU architecture – e.g. NVIDIA Tesla
Tesla – processing power ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tesla C1060 memory (from: M A Martinez-del-Amor et al. (2008) based on E Lindholm et al. (2008))
Programming GPUs – CUDA and OpenCL ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
First step – obtaining and installing CUDA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Host (CPU) – Device (GPU) Relationship ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Organisation of threads on GPU ,[object Object],[object Object],[object Object],[object Object],[object Object]
Memory hierarchy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
CUDA terminology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Application to Monte Carlo simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Random Number Generators: choice of algorithm ,[object Object],[object Object],[object Object],[object Object]
MRG32k3a: skip ahead ,[object Object],[object Object],[object Object]
MRG32k3a: modulus ,[object Object],[object Object],[object Object],[object Object],[object Object]
MRG32k3a: memory coalescence ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
MRG32k3a: single – double precision ,[object Object],[object Object],[object Object],[object Object]
MRG32k3a: GPU benchmarking – double precision ,[object Object],[object Object],[object Object],[object Object],[object Object],GPU CPU-ICC CPU-VC++ VSL-ICC VSL-VC++ Samples/ sec 3.00E+09 3.46E+07 4.77E+07 9.35E+07 9.32E+07
MRG32k3a: GPU benchmarking – single precision ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],GPU CPU-ICC CPU-VC++ VSL-ICC VSL-VC++ Samples/ sec 3.49E+09 3.58E+07 5.24E+07 1.02E+08 9.75E+07
LIBOR Market Model on GPU ,[object Object],[object Object],[object Object]
Numerical Libraries for GPUs ,[object Object],[object Object],[object Object],[object Object],[object Object]
NAG Routines for GPUs
nag_gpu_mrg32k3a_uniform
nag_gpu_mrg32k3a_uniform
nag_gpu_mrg32k3a_uniform
Example program: generate random numbers on GPU ,[object Object],[object Object]
NAG Routines for GPUs
nag_gpu_mrg32k3a_next_uniform
nag_gpu_mrg32k3a_next_uniform
Example program – kernel function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Library issues: Auto-tuning ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Early Success with BNP Paribas
BNP Paribas Results – local vol example
[object Object],And with Bank of America Merrill Lynch
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],“ A N Other Tier 1” Risk Group
NAG routines for GPUs – 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
NAG routines for GPUs – 2 ,[object Object],[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object],[object Object]
Acknowledgments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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