Accelerating the Calibration of Stochastic Volatility Models PDF Download
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Author: Fiodar Kilin
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Author: Fiodar Kilin
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
Author: Matthew Francis Dixon
Publisher:
ISBN:
Category :
Languages : en
Pages : 6
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Book Description
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 OpenMP, OpenCL, CUDA, or SIMD 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 productionization.This paper describes the acceleration of stochastic volatility model calibration on multi-core CPUs and GPUs using the Xcelerit platform. By adopting a simple dataflow 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 $30$x and $293$x are respectively achieved on an Intel Xeon CPU and NVIDIA Tesla K40 GPU, compared to a sequential CPU implementation. The Xcelerit platform implementation is further shown to be equivalent in performance to a low-level CUDA version. Overall, we are able to reduce the entire calibration process time of the sequential implementation from 6,189 seconds to 183.8 and 17.8 seconds on the CPU and GPU respectively without requiring the developer to reimplement in low-level high performance computing frameworks.
Author: Matthew Francis Dixon
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
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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 mid-market 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.
Author: André Bernemann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Pricing and risk analysis for today's exotic structured equity products is computationally more and more demanding and time consuming. GPUs offer the possibility to significantly increase computing performance even at reduced costs. We applied this technology to replace a large amount of our CPU based computing grid by hybrid GPU/CPU pricing engines. One GPU based pricing engine with two Tesla C1060 replaced 140 CPU cores in performing Monte Carlo based simulation of our productive structured equity portfolio with the local and stochastic volatility models. Instantaneous calibration of the piecewise timedependent Heston model on a single GPU is enabled.
Author: Matthew Francis Dixon
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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In this paper we describe our work on speeding up the Heston stochastic volatility model calibration, a financial application, on GPUs. The Heston volatility model is used extensively across the capital markets to price and measure the market risk of exchange traded financial options. When fitted to sub-minute level market mid-price quotes, the model may require frequent calibration every few minutes. The R statistical software package is easy to use and is popular with quantitative analysts in the financial industry. However, a typical R based implementation of the Heston Model calibration on a CPU does not meet the performance requirements for sub-minute level trading, i.e. mid to high frequency trading. The calibration of a Heston model is performed over M option data points which remains fixed during the calibration computation. A typical organization of this computation involves calling an optimization routine with a pointer to ErrorFunction() which estimates the error between market observed and model option prices. We implemented the calibration computation in R and observed that the computation time is dominated by the calculation of the ErrorFunction(). This paper describes the implementation of a GPU optimized kernel for this computation that can be called by the R script performing the calibration process. For M=1024 we demonstrate a factor of 760x improvement in the overall calibration time over the R sequential implementation by off-loading ErrorFunction() on a system with an Intel Core i5 processor and NVIDIA Tesla K20c (Kepler architecture) consisting of 2496 cores. Note that not all the performance gain is due to the GPU - partly it is due to the reduction in the overhead of R for the Heston model calculation. For comparison we also implemented the calibration code using C. We observed a speed up of 230x for the GPU based implementation over the C version indicating that a factor of 3.4x improvement is due to avoiding the R overhead for the Heston Model Calculation. However, the overall calibration time using R based optimization routines combined with the GPU off-loaded ErrorFunction() is comparable to a C GPU based calibration code.
Author: Matthew Francis Dixon
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
Low-latency real-time option analytics feeds provide tick-by-tick implied volatilities and greeks based on exchange data. In order for the Black-Scholes implied volatility surface to exhibit the empirically observed skew or smile, a stochastic volatility model can be used to compute the option greeks. Because the European price under many stochastic volatility models only exists in semi-analytic form, frequent robust calibration of the model is computationally prohibitive. This paper explores three parallelization approaches for calibrating stochastic volatility models deployed on a multicore CPU cluster. The contribution of this paper is to provide benchmarks demonstrating hybrid shared and distributed memory parallelization techniques using Python packages for robust calibration of stochastic volatility models. The focus here will be on the Heston and Bates models, but the results in this paper generalize to any of the exponential Levy models incorporating stochastic volatility and jumps and whose characteristic function can be expressed in closed form. We evaluated the performance for our implementation on a cluster of 32 dual socket Dell PowerEdge R410 nodes providing 256 cores in total. Using distributed memory parallelization, we obtain a speedup of up to 139x against the sequential version of the calibration error function evaluation and reduce the overall time taken to calibrate a chain of 1024 SPX options by a factor of 37x.
Author: Christian Bayer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Sparked by Alòs, León und Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson und Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz und Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models such as Heston (1993), these non-Markovian models with fractional volatility drivers allow to parsimoniously recover key stylized facts of market implied volatility surfaces such as the exploding power-law behaviour of the at-the-money volatility skew as time to maturity goes to zero. Standard model calibration routines rely on the repetitive evaluation of the map from model parameters to Black-Scholes implied volatility, rendering calibration of many (rough) stochastic volatility models prohibitively expensive since there the map can often only be approximated by costly Monte Carlo (MC) simulations (Bennedsen, Lunde & Pakkanen, 2017; McCrickerd & Pakkanen, 2018; Bayer et al., 2016; Horvath, Jacquier & Muguruza, 2017). As a remedy, we propose to combine a standard Levenberg-Marquardt calibration routine with neural network regression, replacing expensive MC simulations with cheap forward runs of a neural network trained to approximate the implied volatility map. Numerical experiments confirm the high accuracy and speed of our approach.
Author: Urij Dolgov
Publisher:
ISBN:
Category :
Languages : de
Pages :
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Author: Fabrice D. Rouah
Publisher: John Wiley & Sons
ISBN: 111900330X
Category : Business & Economics
Languages : en
Pages : 359
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Book Description
Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.
Author: Fan Wang
Publisher:
ISBN: 9781303065750
Category :
Languages : en
Pages : 112
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Book Description
In this thesis we study carefully the stochastic local volatility (SLV) model for pricing barrier options in foreign exchange or equity market. We first discuss the advantage and disadvantage of popular models such as stochastic volatility and local volatility that have been used for pricing the same products, then introduce the necessities to build a hybrid SLV model. We classified the calibration process of SLV model into two major parts according to parameters' different nature, and point out the slowness of the calibration procedure is mainly caused by solving the lever-age surface from Kolmogorov forward equation via the iteration method. Our major contribution is to apply the fast mean reversion volatility modeling technique and singular/regular perturbation analysis developed by Fouque, Papanicolaou, Sircar and Sølna in [24, 27, 26] to the forward equation, which gives a starting point which is proved to be close to the true solution, so that the iteration time is significantly reduced. Besides, we developed target functions specifically designed for processing exotic option quotes and give suitable numerical methods for each step of the calibration.
