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.
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.
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.
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.
Download or read book Essays on Stochastic Volatility Models with Jump Clustering written by Jian Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Multiple Time Scales Stochastic Volatility Modeling Method in Heath jarrow morton Model of Interest Rate Market written by Feiyue Di and published by . This book was released on 2011 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: We utilize multiple time scales processes in consistent dynamic modeling to capture main time scales and heterogeneity features of the volatility process of Heath-Jarrow-Moton models in the fixed income market. The Black-Scholes type HJM models are prevailing in both industry and academy. However since these models assume that the volatility process of the underlying financial contract is constant during the term period, they are not able to incorporate some implied volatility phenomenons emerging after the Crash of 1987. Stochastic volatility modeling is one of the main approach to overcome the above defects of the Black-Scholes type models. By applying the time scale separation, that is, the singular perturbation method, we show that the stochastic volatility HJM model we proposed are parsimonious and robust effective models. In fact, we carry out this framework on the linear finite dimensional realizable HJM models, derive the explicit pricing formulas of floorlet contracts under this stochastic volatility HJM models and estimate the accuracy of the result. Meanwhile, as a specific example, we studied the stochastic volatility Hull-White model explicitly. Besides the pricing function of the floorlet contracts, we also obtain the explicit form of the pricing function of the swaption. Following the calibration procedures we proposed, we calibrated this model by a group of daily swaption data from PIMCO. The calibration result shows that the mutliple time scales stochastic volatility Hull-White model is able to capture the implied volatility smile and this model is stable statically.
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:
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:
Download or read book A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics written by Alexey Medvedev and published by . This book was released on 2003 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local Stochastic Volatility Models written by Cristian Homescu and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models. We describe calibration procedures, with special attention given to usage and solution of corresponding forward Kolmogorov PDE/PIDE, and outline powerful algorithms for estimation of model parameters. Emphasis is placed on presenting practical details regarding the setup and the numerical solution of both forward and backward PDEs/PIDEs obtained from the LSV models. Consequently we discuss specifics (based on our experience and best practices from literature) regarding choice of boundary conditions, construction of nonuniform spatial grids and adaptive temporal grids, selection of efficient and appropriate finite difference schemes (with possible enhancements), etc. We also show how to practically integrate specific features of various types of financial instruments within calibration and pricing settings. We consider all questions and topics identified as most relevant during the selection, calibration and pricing procedures associated with local stochastic volatility models, providing answers (to the best of our knowledge), and present references for deeper understanding and for additional perspectives. In a nutshell, it is our intention to present here an effective roadmap for a successful LSV journey.
Download or read book Computing Journal written by Anna Pretre and published by . This book was released on 2015 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we compare different models describing the implied volatility surface. In particular we analyse in-depth the numerical properties of the Heston model and we extend it to include Jump processes. In our approach, we first identify a closed-form solution or a closest proxy of it, we then price contingent claims testing correctness and efficiency of the numerical solution against the closed-form solution, finally the numerical solution is adapted to American-option pricing.For each model, the closed-form solution is obtained from the stochastic differential equation and the numerical solution is worked out from the integropartial-differential equation. In all cases the scaling behavior and the effective parameter range in practical cases is addressed.
Download or read book Calibration of Heston s Stochastic Volatility Model Using the Extended Kalman Filter written by and published by . This book was released on 2007 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calibration of local volatility models and proper orthogonal decomposition reduced order modeling for stochastic volatility models written by Jian Geng and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Volatility for Real written by Jesper Andreasen and published by . This book was released on 2006 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We combine classical ideas of separable volatility structures in the HJM framework with the latest techniques for calibration of stochastic volatility models and create a new class of efficient multi-factor term structure models with stochastic volatility. These models have the flexibility of as the Libor market models but the speed of the short rate models.
Download or read book Novel Methods in Computational Finance written by Matthias Ehrhardt and published by Springer. This book was released on 2017-09-19 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2003 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
