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 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 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 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 From Moving Average Local and Stochastic Volatility Models to 2 Factor Stochastic Volatility Models written by Oleg Kovrizhkin and published by . This book was released on 2008 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the following models:1. Generalization of a local volatility model rolled with a moving average of the spot: dS = mu Sdt + sigma(S/A)SdW$ where A(t) is a moving average of spot S.2. Generalization of Heston pure stochastic volatility model rolled with a moving average of the stochastic volatility: dS = mu Sdt + sigma SdW, dsigma^2 = k(theta - sigma^2)dt + gamma sigma dZ where theta(t) is a moving average of variance sigma^2.3. Generalization of a full stochastic volatility with the process for volatility depending on both sigma and S and rolled with a moving average of S: dS = mu Sdt + sigma SdW, dsigma = a(sigma, S/A)dt + b(sigma, S/A)dZ,corr(dW, dZ) = rho(sigma, S/A)$, where A(t) is a moving average of the spot S. We will generalize these and other ideas further and show that they lead to a 2-factor pure stochastic volatility model: dS = mu Sdt + sigma SdW$, sigma = sigma(v_1, v_2), dv_1 = a_1(v_1, v_2)dt + b_1(v_1, v_2)dZ_1,dv_2 = a_2(v_1, v_2)dt + b_2(v_1, v_2)dZ_2, corr(dW, dZ_1) = rho_1(v_1, v_2), corr(dW, dZ_2) = rho_2(v_1, v_2), corr(dZ_1, dZ_2) = rho_3(v_1, v_2) and give examples of analytically solvable models, applicable for multicurrency models consistent with cross currency pairs dynamics in FX. We also consider jumps and stochastic interest rates.

Download or read book Handbook Of Energy Finance Theories Practices And Simulations written by Stephane Goutte and published by World Scientific. This book was released on 2020-01-30 with total page 827 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling the dynamics of energy markets has become a challenging task. The intensification of their financialization since 2004 had made them more complex but also more integrated with other tradable asset classes. More importantly, their large and frequent fluctuations in terms of both prices and volatility, particularly in the aftermath of the global financial crisis 2008-2009, posit difficulties for modeling and forecasting energy price behavior and are primary sources of concerns for macroeconomic stability and general economic performance.This handbook aims to advance the debate on the theories and practices of quantitative energy finance while shedding light on innovative results and technical methods applied to energy markets. Its primary focus is on the recent development and applications of mathematical and quantitative approaches for a better understanding of the stochastic processes that drive energy market movements. The handbook is designed for not only graduate students and researchers but also practitioners and policymakers.

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 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 Smooth Calibration in Local Volatility with Jumps written by Gilles Boya and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this article is to provide tools to calibrate a smooth local volatility surface in the presence of jumps. First we provide techniques to approximate the value of European options in a local volatility model with jumps, then we propose a quick and robust fixed point algorithm combined with this method to build smooth local volatility surfaces.

Download or read book Local Volatility Models Enhanced with Jumps written by Hamza Guennoun and published by . This book was released on 2016 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the calibration to market call prices C^{mkt}(t;K) of a local volatility model enhanced with jumps. Instead of giving an exact calibration condition on the local volatility, we introduce an approximate process S_t^ epsilon satisfying a well-defined nonlinear McKean SDE driven by a Cox process, such that E[(S_t^ epsilon - K) _ ] converges to C^{mkt}(t;K) as epsilon goes to 0 for all (t;K). This implies that the particle method, applied to the process S_t^ epsilon, which is used for the calibration of the local volatility, converges numerically. We illustrate the accuracy of our calibration algorithm with various numerical experiments. Finally, we extend this model by allowing jumps in the local 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 Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

Download or read book The Volatility Smile written by Emanuel Derman and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.

Download or read book Topics in Volatility Models written by Cong Yi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis I will present my PhD research work, focusing mainly on financialmodelling of asset?s volatility and the pricing of contingent claims (financial derivatives), which consists of four topics:1. Several changing volatility models are introduced and the pricing of Europeanoptions is derived under these models;2. A general local stochastic volatility model with stochastic interest rates (IR)is studied in the modelling of foreign exchange (FX) rates. The pricing of FXoptions under this model is examined through the use of an asymptotic expansionmethod, based on Watanabe-Yoshida theory. The perfect/partial hedging issuesof FX options in the presence of local stochastic volatility and stochastic IRs arealso considered. Finally, the impact of stochastic volatility on the pricing of FX-IRstructured products (PRDCs) is examined;3. A new method of non-biased Monte Carlo simulation for a stochastic volatilitymodel (Heston Model) is proposed;4. The LIBOR/swap market model with stochastic volatility and jump processesis studied, as well as the pricing of interest rate options under that model. In conclusion, some future research topics are suggested. Key words: Changing Volatility Models, Stochastic Volatility Models, LocalStochastic Volatility Models, Hedging Greeks, Jump Diffusion Models, ImpliedVolatility, Fourier Transform, Asymptotic Expansion, LIBOR Market Model, MonteCarlo Simulation, Saddle Point Approximation.

Download or read book Stochastic Volatility Models with Jumps and High Frequency Data written by Jonas Kau and published by . This book was released on 2009 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility Model with Jumps in Returns and Volatility written by Adjoa K. Numatsi and published by . This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A New Class of Stochastic Volatility Models with Jumps Theory and Estimation written by CIRANO. and published by Montréal : CIRANO. This book was released on 1999 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: