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Short Term At The Money Asymptotics Under Stochastic Volatility Models
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Book Synopsis Short-Term At-the-Money Asymptotics Under Stochastic Volatility Models by : Omar El Euch
Download or read book Short-Term At-the-Money Asymptotics Under Stochastic Volatility Models written by Omar El Euch and published by . This book was released on 2019 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.
Book Synopsis Approximation and Calibration of Short-term Implied Volatilities Under Jump-diffusion Stochastic Volatility by : Alexey Medvedev
Download or read book Approximation and Calibration of Short-term Implied Volatilities Under Jump-diffusion Stochastic Volatility written by Alexey Medvedev and published by . This book was released on 2006 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Implied Volatility Asymptotics Under Affine Stochastic Volatility Models by : Antoine Jacquier
Download or read book Implied Volatility Asymptotics Under Affine Stochastic Volatility Models written by Antoine Jacquier and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Methods for Computing Implied Volatilities Under Stochastic Volatility by : Alexey Medvedev
Download or read book Asymptotic Methods for Computing Implied Volatilities Under Stochastic Volatility written by Alexey Medvedev and published by . This book was released on 2008 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose an analytical formula for computing implied volatilities of European options based on their short term asymptotics. The analysis is performed in a general framework with local and stochastic volatility. Assuming CEV volatility of volatility we first obtain a quasi-analytical solution for the limit of implied volatilities as time-to-maturity goes to zero (instanteneous implied volatility). Then we develop our analytical formula in the form of a local transformation of the instanteneous implied volatility. Numerical experiments suggests that this approximation is extremely accurate at short maturities (one or two month). We further introduce a class of models under which this method is accurate even for long maturity options. In the particular case of SABR model we improve the formula derived in Hagan et al. (2002).
Book Synopsis Stochastic Volatility Models by : Jian Yang
Download or read book Stochastic Volatility Models written by Jian Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Skew Under Stochastic Volatility by : Antoine (Jack) Jacquier
Download or read book Asymptotic Skew Under Stochastic Volatility written by Antoine (Jack) Jacquier and published by . This book was released on 2007 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to improve and discuss the asymptotic formula of the implied volatility (when maturity goes to infinity) derived by A.Lewis. Indeed, we are here able to provide more accurate at-the-money asymptotics. Such analytic formulas are useful for calibration.
Book Synopsis Asymptotic Chaos Expansions in Finance by : David Nicolay
Download or read book Asymptotic Chaos Expansions in Finance written by David Nicolay and published by Springer. This book was released on 2014-11-25 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.
Book Synopsis Stochastic Volatility in Financial Markets by : Fabio Fornari
Download or read book Stochastic Volatility in Financial Markets written by Fabio Fornari and published by Springer Science & Business Media. This book was released on 2000-05-31 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting advanced topics in financial econometrics and theoretical finance, this guide is divided into three main parts.
Book Synopsis Options - 45 Years Since The Publication Of The Black-scholes-merton Model: The Gershon Fintech Center Conference by : David Gershon
Download or read book Options - 45 Years Since The Publication Of The Black-scholes-merton Model: The Gershon Fintech Center Conference written by David Gershon and published by World Scientific. This book was released on 2022-12-21 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions by the best-known and consequential researchers who, over several decades, shaped the field of financial engineering. It presents a comprehensive and unique perspective on the historical development and the current state of derivatives research. The book covers classical and modern approaches to option pricing, realized and implied volatilities, classical and rough stochastic processes, and contingent claims analysis in corporate finance. The book is invaluable for students, academic researchers, and practitioners working with financial derivatives, market regulation, trading, risk management, and corporate decision-making.
Book Synopsis Second Order Multiscale Stochastic Volatility Asymptotics by : Jean-Pierre Fouque
Download or read book Second Order Multiscale Stochastic Volatility Asymptotics written by Jean-Pierre Fouque and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{ o}lna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions -- one fast mean-reverting and one slow-varying, and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that, to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.
Book Synopsis Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model by : Mohammed Albuhayri
Download or read book Asymptotics of Implied Volatility in the Gatheral Double Stochastic Volatility Model written by Mohammed Albuhayri and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Stochastic Volatility Models by : Max Souza
Download or read book Asymptotic Behavior of Stochastic Volatility Models written by Max Souza and published by . This book was released on 2005 with total page 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 Inverse Problems and Asymptotics for Stochastic Volatility Models by :
Download or read book Inverse Problems and Asymptotics for Stochastic Volatility Models written by and published by . This book was released on 2006 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modelling and Simulation of Stochastic Volatility in Finance by : Christian Kahl
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.
Book Synopsis Modeling Stochastic Volatility with Application to Stock Returns by : Mr.Noureddine Krichene
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.
