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Deep Calibration Of Rough Stochastic Volatility Models
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Book Synopsis Deep Calibration of Rough Stochastic Volatility Models by : Christian Bayer
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.
Book Synopsis Accelerating the Calibration of Stochastic Volatility Models by : Fiodar Kilin
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:
Book Synopsis Polynomial Semimartingales and a Deep Learning Approach to Local Stochastic Volatility Calibration by : Wahid Khosrawi-Sardroudi
Download or read book Polynomial Semimartingales and a Deep Learning Approach to Local Stochastic Volatility Calibration written by Wahid Khosrawi-Sardroudi and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Financial markets have experienced a precipitous increase in complexity over the past decades, posing a significant challenge from a risk management point of view. This complexity motivates the application and development of sophisticated models based on the theory of stochastic processes and in particular stochastic calculus. In this regard, the contribution of this thesis is twofold, namely by extending the class if tractable stochastic processes in form of polynomial processes and polynomial semimartingales and by showing how efficient calibration of local stochastic volatility models is possible by applying machine learning techniques. In the first part - the main part - we extend the class of polynomial processes that has previously been established to include beyond stochastic discontinuity. This extension is motivated by the fact that certain events in financial markets take place at a deterministic time point but without foreseeable outcome. Such events consist e.g. of decisions regarding interest rates of central banks or political elections/votes. Since the outcome has a significant impact on markets, it is therefore desirable to consider stochastic processes, that can reproduce such jumps at previously specified time points. Such an extension has already been introduced in the affine framework. We will show that similar modifications hold true in the polynomial case. In particular, we will show how after this extension, computation of mixed moments in a multivariate setting reduces to solving a measure ordinary differential equation, posing a significant reduction in complexity to the measure partial differential case in the context of Kolmogorow equations. A central role in the theory of time-homogeneous polynomial processes is played by the theory of one parameter matrix semigroups. Hence, we will develop a two parameter version of the matrix semigroup theory under lower regularity then what exists in the literature. This accounts for time-inhomogeneity of the stochastic processes we consider. While in the one parameter case, full regularity follows already from very mild assumptions, we will see that this is not the case anymore in the two parameter case. In the second part of this thesis we investigate a more applied topic, namely the exact calibration of local stochastic volatility models to financial data. We show how this computationally challenging problem can be efficiently solved by applying machine learning te ...
Book Synopsis Rough Volatility by : Christian Bayer
Download or read book Rough Volatility written by Christian Bayer and published by SIAM. This book was released on 2023-12-18 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves essentially as a fractional Brownian motion with a small Hurst parameter. The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression. This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.
Book Synopsis Log-modulated Rough Stochastic Volatility Models by : Christian Bayer
Download or read book Log-modulated Rough Stochastic Volatility Models written by Christian Bayer and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rough Volatility Models by : Henry Stone
Download or read book Rough Volatility Models written by Henry Stone and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Volatility Models by : Warrick Poklewski-Koziell
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:
Book Synopsis Local Stochastic Volatility Models by : Cristian Homescu
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.
Book Synopsis Calibration of Stochastic Volatility Models on a Multi-Core CPU Cluster by : Matthew Francis Dixon
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.
Book Synopsis Deep PPDEs for Rough Local Stochastic Volatility by : Antoine (Jack) Jacquier
Download or read book Deep PPDEs for Rough Local Stochastic Volatility written by Antoine (Jack) Jacquier and published by . This book was released on 2019 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the notion of rough local stochastic volatility models, extending the classical concept to the case where volatility is driven by some Volterra process. In this setting, we show that the pricing function is the solution to a path-dependent PDE, for which we develop a numerical scheme based on Deep Learning techniques. Numerical simulations suggest that the latter is extremely efficient, and provides a good alternative to classical Monte Carlo simulations.
Book Synopsis A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics by : Alexey Medvedev
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:
Book Synopsis Large Deviations and Asymptotic Methods in Finance by : Peter K. Friz
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Book Synopsis Large Deviations for Rough and Complete Stochastic Volatility Models by : Chloe Alice Lacombe
Download or read book Large Deviations for Rough and Complete Stochastic Volatility Models written by Chloe Alice Lacombe and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Calibration of local volatility models and proper orthogonal decomposition reduced order modeling for stochastic volatility models by : Jian Geng
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:
Book Synopsis Vol-of-Vol Expansion for (Rough) Stochastic Volatility Models by : Ozan Akdogan
Download or read book Vol-of-Vol Expansion for (Rough) Stochastic Volatility Models written by Ozan Akdogan and published by . This book was released on 2019 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, explicit (in the sense of non-recursive) representations of the so-called push-down Malliavin weights that utilizes a precise understanding of the terms of this expansion.
Book Synopsis A Portable and Fast Stochastic Volatility Model Calibration Using Multi and Many-Core Processors by : Matthew Francis Dixon
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.
Book Synopsis Handbook of Volatility Models and Their Applications by : Luc Bauwens
Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-04-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
