Calibration of Stochastic Volatility Models on a Multi-Core CPU Cluster

Dixon, Matthew; Zubair, Mohammed

doi:10.2139/ssrn.2349333

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…Also the methodology is not limited to the 14 integration methods presented here, but can be extended to other integration methods, for example, quadrature or FFT-based. Examples are the popular Fourier-Cosine Method by Fang and Oosterlee [20], which has shown to have superior convergence parameters over the Carr-Madan FFT method [21] and does not require a damping parameter.…”

Section: Discussion and Extensionsmentioning

confidence: 99%

Precision‐tuning and hybrid pricer for closed‐form solution‐based Heston calibration

Brugger

Liu

Schryver

et al. 2015

Concurrency and Computation

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SUMMARYCalibration methods are the heart of modeling any financial process. While for the Heston model (semi) closed-form solutions exist for simple products, their evaluation involves complex functions and infinite integrals. So far, these integrals can only be solved with time-consuming numerical methods. For that reason, calibration consumes a large portion of available compute power in the daily finance business.However, more and more theoretical and practical subtleties have been discovered over the years, and today, a large number of calibration methods are available. Currently, there is no clear indication which numerical method should be used for a specific calibration purpose under given speed and accuracy constraints. With this publication, we aim at closing this gap. We derive a novel methodology for systematically finding the best methods for a well-defined accuracy target. For a practical setup, we study the available popular closed-form solutions and integration algorithms. In total, we compare 14 numerical methods, including adaptive quadrature and Fourier methods. For a target accuracy of 10 3 , we show that adaptive GaussKronrod methods are best on CPUs for the unrestricted parameter set. Furthermore, we introduce hybrid pricer methods that combine quadrature and fast Fourier transform pricers, what gives us another 2:4 speedup.

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Section: Discussion and Extensionsmentioning

confidence: 99%

Precision‐tuning and hybrid pricer for closed‐form solution‐based Heston calibration

Brugger

Liu

Schryver

et al. 2015

Concurrency and Computation

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show abstract

“…Following Fang and Oosterlee , the entire inverse Fourier integral in Equation is reconstructed from Fourier‐cosine series expansion of the integrand to give the following approximation of the call price

C (S_{0}, K, τ; {boldz}_{0}) \approx K e^{- rτ} R ([], \sum_{k = 0}^{N - 1} ϕ ((), \frac{kπ}{b - a}; {boldz}_{0}) e^{ikπ \frac{x - a}{b - a}} U_{k}),

where x := ln( S 0 / K ) and ϕ ( w ; z 0 ) denotes the Heston characteristic function of the log‐asset price, U k the payoff series coefficients and N denotes the number of terms in the cosine series expansion (typically 128 will suffice). The Fourier‐cosine approach is shown to be superior in convergence properties to other fast Fourier transform and quadrature based methods in .…”

Section: Example: Heston Modelmentioning

confidence: 99%

“…Dixon and Zubair and Dixon, Khan, and Zubair approach the problem from a parallel architecture and software engineering perspective motivated by . Starting from the premise that implementation of financial models in high‐level programming environments and languages such as R and Python is conducive to design exploration, rapid prototyping, and model validation, the authors evaluate parallel implementations of the calibration designed for clusters of multi‐core CPUs and GPUs.…”

Section: Introductionmentioning

confidence: 99%

A portable, extensible and fast stochastic volatility model calibration using multi and many‐core processors

Dixon

Lotze²,

Zubair

2015

Concurrency and Computation

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Summary Financial markets change precipitously, and on‐demand pricing and risk models must be constantly recalibrated to reduce risk. However, certain classes of models are computationally intensive to robustly calibrate to intraday prices – stochastic volatility models being an archetypal example due to the non‐convexity of the objective function. In order to accelerate this procedure through parallel implementation, financial application developers are faced with an ever growing plethora of low‐level high‐performance computing frameworks such as Open Multi‐Processing, Open Computing Language, compute unified device architecture, or single instruction multiple data intrinsics, and forced to make a trade‐off between performance versus the portability, flexibility, and modularity of the code required to facilitate rapid in‐house model development and productionisation. This paper describes the acceleration of stochastic volatility model calibration on multi‐core CPUs and graphics processing units (GPUs) using the Xcelerit platform. By adopting a simple programming model, the Xcelerit platform enables the application developer to write sequential, high‐level C++ code, without concern for low‐level high‐performance computing frameworks. This platform provides the portability, flexibility, and modularity required by application developers. Speedups of up to 30x and 293x are respectively achieved on an Intel Xeon CPU and NVIDIA Tesla K40 GPU, compared with a sequential CPU implementation. The Xcelerit platform implementation is further shown to be equivalent in performance to a low‐level compute unified device architecture version. Overall, we are able to reduce the entire calibration process time of the sequential implementation from 6189 to 183.8 and 17.8 s on the CPU and GPU, respectively, without requiring the developer to reimplement in low‐level high‐performance computing frameworks. Copyright © 2015 John Wiley & Sons, Ltd.

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“…where x := ln(S 0 /K) and φ(w; z 0 ) denotes the Heston characteristic function of the log-asset price, U k the payoff series coefficients and N denotes the number of terms in the cosine series expansion (typically 128 will suffice). For this approximation of the Heston model call price, the Fourier-Cosine approach is shown to be superior in convergence properties to other FFT and quadrature based methods in [6].…”

Section: Pricingmentioning

confidence: 99%

“…The global optimizers that the authors consider include the differential evolution (DE) algorithm and simulated annealing (SA), both of which have been employed elsewhere in the quantitative finance literature [2]. Dixon and Zubair [6] consider the calibration of a Bates model, a slightly more generalized form of the Heston model which includes jumps, using python and compare the performance tradeoffs of using the mpi4py and multicore python packages to parallelize computations on a multi-core CPU cluster. Here, in this paper, we depart from both of these works by presenting a R package for off-loading a variety of stochastic volatility model computations onto the GPU.…”

Section: Introductionmentioning

confidence: 99%

<i>gpusvcalibration</i>: A R Package for Fast Stochastic Volatility Model Calibration Using GPUs

2014

Self Cite

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In this paper we describe the gpusvcalibration R package for accelerating stochastic volatility model calibration on GPUs. The package is designed for use with existing CRAN packages for optimization such as DEOptim and nloptr. Stochastic volatility models are used extensively across the capital markets for pricing and risk management of exchange traded financial options. However, there are many challenges to calibration, including comparative assessment of the robustness of different models and optimization routines. For example, we observe that when fitted to sub-minute level midmarket quotes, models require frequent calibration every few minutes and the quality of the fit is routine sensitive. The R statistical software environment is popular with quantitative analysts in the financial industry partly because it facilitates application design space exploration. However, a typical R based implementation of a stochastic volatility model calibration on a CPU does not meet the performance requirements for sub-minute level trading, i.e. mid to high frequency trading. We identified the most computationally intensive part of the calibration process in R and off-loaded that to the GPU. We created a map-reduce interface to the computationally intensive kernel so that it can be easily integrated in a variety of R based calibration codes using our package. We demonstrate that the new R based implementation using our package is comparable in performance to a C/C ++ GPU based calibration code.

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Calibration of Stochastic Volatility Models on a Multi-Core CPU Cluster

Cited by 4 publications

References 9 publications

Precision‐tuning and hybrid pricer for closed‐form solution‐based Heston calibration

Precision‐tuning and hybrid pricer for closed‐form solution‐based Heston calibration

A portable, extensible and fast stochastic volatility model calibration using multi and many‐core processors

<i>gpusvcalibration</i>: A R Package for Fast Stochastic Volatility Model Calibration Using GPUs

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