Download or read book Turbo Charged Local Stochastic Volatility Models written by Ghislain Vong and published by . This book was released on 2013 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article presents an alternative formulation of the standard Local Stochastic Volatility model (LSV) widely used for the pricing and risk-management of FX derivatives and to a lesser extent of equity derivatives. In the standard model, calibration is achieved by solving a non-linear two-factor Kolmogorov forward PDE, where a minimum number of vol points is required to achieve convergence of a finite difference implementation. In contrast, we propose to model the volatility process by a Markov chain defined over an arbitrary small number of states, so that calibration and pricing are achieved by solving a coupled system of one-factor PDEs. The practical benefits are twofolds: existing one-factor PDE solvers can be recycled to model stochastic volatility, while the reduction in number of discretisation points implies a speedup in execution time that enables real-time risk-management of large derivatives position.

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 Local Stochastic Volatility written by Lorenzo Bergomi and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine local-stochastic volatility models and derive a simple condition such models need to obey so that the carry P&L of a delta-hedged/vega-hedged position makes sense in a trading context.We give examples of admissible and non-admissible models and discuss the issue of the delta position in the hedge portfolio.We end with a characterization of the break-even levels of the local volatility model - itself in the admissible class.

Download or read book Rough PDEs for Local Stochastic Volatility Models written by Peter Bank and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time-inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely understand the conditional LSV dynamics and reveal their Markovian nature. The latter allows us to connect the conditional dynamics to so-called rough partial differential equations (RPDEs), through a Feynman-Kac type of formula. In terms of European pricing, conditional on realizations of one Brownian motion, we can compute conditional option prices by solving the corresponding linear RPDEs, and then average over all samples to find unconditional prices. Our approach depends only minimally on the specification of the volatility, making it applicable for a wide range of classical and rough LSV models, and it establishes a PDE pricing method for non-Markovian models. Finally, we present a first glimpse at numerical methods for RPDEs and apply them to price European options in several rough LSV models.

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

Download or read book FX Barrier Options written by Zareer Dadachanji and published by Springer. This book was released on 2016-04-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Barrier options are a class of highly path-dependent exotic options which present particular challenges to practitioners in all areas of the financial industry. They are traded heavily as stand-alone contracts in the Foreign Exchange (FX) options market, their trading volume being second only to that of vanilla options. The FX options industry has correspondingly shown great innovation in this class of products and in the models that are used to value and risk-manage them. FX structured products commonly include barrier features, and in order to analyse the effects that these features have on the overall structured product, it is essential first to understand how individual barrier options work and behave. FX Barrier Options takes a quantitative approach to barrier options in FX environments. Its primary perspectives are those of quantitative analysts, both in the front office and in control functions. It presents and explains concepts in a highly intuitive manner throughout, to allow quantitatively minded traders, structurers, marketers, salespeople and software engineers to acquire a more rigorous analytical understanding of these products. The book derives, demonstrates and analyses a wide range of models, modelling techniques and numerical algorithms that can be used for constructing valuation models and risk-management methods. Discussions focus on the practical realities of the market and demonstrate the behaviour of models based on real and recent market data across a range of currency pairs. It furthermore offers a clear description of the history and evolution of the different types of barrier options, and elucidates a great deal of industry nomenclature and jargon.

Download or read book Explicit Implied Volatilities for Multifactor Local Stochastic Volatility Models written by Matthew Lorig and published by . This book was released on 2014 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, 3/2 stochastic volatility, and SABR local-stochastic volatility.

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.

Download or read book Stochastic Volatility and Realized Stochastic Volatility Models written by Makoto Takahashi and published by Springer Nature. This book was released on 2023-04-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.

Download or read book Local Stochastic Volatility with Jumps written by Stefano Pagliarani and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

Download or read book A Hybrid Stochastic Volatility Model Incorporating Local Volatility written by Yu Tian and published by . This book was released on 2014 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the flexibility for pricing exotic options. The difficulty in implementing the SLV model lies in the calibration of the leverage function, which can be roughly seen as a ratio between the local volatility and the conditional expectation of stochastic volatility. We will illustrate our implementation of the SLV model and show the pricing performance for exotic options.

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 ...

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by . This book was released on 2016 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well as approximations for skew and curvature. Exact and approximate techniques for taking dividends into account are presented.We then turn to the dynamics of the local volatility model. We introduce the Skew Tickiness Ratio (SSR) and derive approximate formulas for the SSR and volatilities of volatilities in the local volatility model.We also examine future skews.We then consider the delta and carry P&L of a hedged option position. We derive the expression of the market-model delta of the local volatility model and discuss the relationship between sticky-strike and market-model deltas. We characterize the gamma/theta break-even levels of a hedged position and show that the local volatility model is indeed a market model.We then derive the expression of the vega-hedge portfolio.Markov-functional models are considered next.Finally, we survey the Uncertain Volatility Model and its usage.A digest summarizes key points.

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 RKHS Regularization of Singular Local Stochastic Volatility McKean Vlasov Models written by Christian Bayer and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the challenges related to the calibration of financial models, we consider the problem of solving numerically a singular McKean-Vlasov equation, which represents a singular local stochastic volatility model. Whilst such models are quite popular among practitioners, unfortunately, its well-posedness has not been fully understood yet and, in general, is possibly not guaranteed at all. We develop a novel regularization approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularized model is well-posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularized model is able to perfectly replicate option prices due to typical local volatility models. Our results are also applicable to more general McKean-Vlasov equations.

Download or read book From Martingale Schrodinger Bridges to a New Class of Stochastic Volatility Model written by Pierre Henry-Labordere and published by . This book was released on 2019 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas and options on realized variance. These models differ strongly from the well-known local stochastic volatility models, in particular the instantaneous volatility-of-volatility of the associated naked SVMs is not modified, once calibrated to market instruments. They can be interpreted as a martingale version of the Schrodinger bridge. The numerical calibration is performed using a dynamic-like version of the Sinkhorn algorithm. We finally highlight a striking relation with Dyson non-colliding Brownian motions.

Download or read book Modeling Stochastic Volatility with Application to Stock Returns written by Mr.Noureddine Krichene and published by International Monetary Fund. This book was released on 2003-06-01 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.