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Author : Fiodar Kilin
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (18 download)
Download or read book Accelerating the Calibration of Stochastic Volatility Models written by Fiodar Kilin and published by . This book was released on 2007 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matthew Francis Dixon
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (13 download)
Download or read book A Portable and Fast Stochastic Volatility Model Calibration Using Multi and Many-Core Processors written by Matthew Francis Dixon and published by . This book was released on 2014 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (13 download)
Download or read book Gpusvcalibration written by Matthew Francis Dixon and published by . This book was released on 2014 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Accelerating Exotic Option Pricing and Model Calibration Using GPUs written by André Bernemann and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (13 download)
Download or read book Accelerating Option Risk Analytics in R Using GPUs written by Matthew Francis Dixon and published by . This book was released on 2014 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (13 download)
Download or read book Calibration of Stochastic Volatility Models on a Multi-Core CPU Cluster written by Matthew Francis Dixon and published by . This book was released on 2013 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Deep Calibration of Rough Stochastic Volatility Models written by Christian Bayer and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 :
Total Pages : pages
Book Rating : 4.:/5 (986 download)
Download or read book Calibration of Heston's stochastic volatility model to an empirical density using a genetic algorithm written by Urij Dolgov and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fabrice D. Rouah
Publisher : John Wiley & Sons
ISBN 13 : 111900330X
Total Pages : 359 pages
Book Rating : 4.1/5 (19 download)
Download or read book The Heston Model and Its Extensions in VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2015-04-27 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 9781303065750
Total Pages : 112 pages
Book Rating : 4.0/5 (657 download)
Download or read book Multiple Time Scales Stochastic Volatility Modeling Method in Stochastic Local Volatility Model Calibration written by Fan Wang and published by . This book was released on 2013 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Christian Kahl
Publisher : Universal-Publishers
ISBN 13 : 1581123833
Total Pages : 219 pages
Book Rating : 4.5/5 (811 download)
Download or read book Modelling and Simulation of Stochastic Volatility in Finance written by Christian Kahl and published by Universal-Publishers. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
Author : Fabien Le Floc'h
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (13 download)
Download or read book Fourier Integration and Stochastic Volatility Calibration written by Fabien Le Floc'h and published by . This book was released on 2014 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We look at recent algorithms to compute Vanilla option prices under the stochastic volatility models with a known characteristic function, focusing on Heston, Bates, Double-Heston, Schobel-Zhu and study how they behave in the calibration of a real-world implied volatility surface example. We consider local minimization based on Levenberg-Marquardt and a smart initial guess, as well global minimization based on differential evolution.
Author : Warrick Poklewski-Koziell
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (824 download)
Download or read book Stochastic Volatility Models written by Warrick Poklewski-Koziell and published by . This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fabrice D. Rouah
Publisher : John Wiley & Sons
ISBN 13 : 1118695178
Total Pages : 437 pages
Book Rating : 4.1/5 (186 download)
Download or read book The Heston Model and its Extensions in Matlab and C# written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
Author : Ricardo Crisóstomo
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (129 download)
Download or read book An Analisys of the Heston Stochastic Volatility Model written by Ricardo Crisóstomo and published by . This book was released on 2014 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : PediaPress
ISBN 13 :
Total Pages : 1231 pages
Book Rating : 4./5 ( download)
Download or read book Financial Derivatives written by and published by PediaPress. This book was released on with total page 1231 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yu Tian
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (11 download)
Download or read book The Hybrid Stochastic-local Volatility Model with Applications in Pricing FX Options written by Yu Tian and published by . This book was released on 2013 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.
