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Author : Max Souza
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (255 download)
Download or read book Asymptotic Behaviour of Stochastic Volatility Models written by Max Souza and published by . This book was released on 2005 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Max Souza
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (931 download)
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:
Author : Hamza Guennoun
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (13 download)
Download or read book Asymptotic Behaviour of the Fractional Heston Model written by Hamza Guennoun and published by . This book was released on 2014 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider here the fractional version of the Heston model originally proposed by Comte, Coutin and Renault. Inspired by some recent ground-breaking work by Gatheral, Jaisson and Rosenbaum, who showed that fractional Brownian motion with short memory allows for a better calibration of the volatility surface (as opposed to the classical econometric approach of long memory of volatility), we provide a characterisation of the short- and long-maturity asymptotics of the implied volatility smile. Our analysis reveals that the short-memory property precisely provides a jump-type behaviour of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit the short-end of the volatility skew.
Author : Archil Gulisashvili
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (13 download)
Download or read book Gaussian Stochastic Volatility Models written by Archil Gulisashvili and published by . This book was released on 2019 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncorrelated Gaussian model grows faster than linearly, then, for the asset price process, all the moments of order greater than one are infinite. Similar moment explosion results are obtained for correlated models.
Author : Fangwei Shi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Asymptotic Analysis of New Stochastic Volatility Models written by Fangwei Shi and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Blanka Horvath
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (13 download)
Download or read book Asymptotic Behaviour of Randomised Fractional Volatility Models written by Blanka Horvath and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail behaviours in particular). In order to do so, we extend some results on sample path large deviations for such diffusions. As an application, we show how these results characterise the small-time and tail estimates of the implied volatility for rough volatility models, recently proposed in mathematical finance.
Author : Omar El Euch
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (13 download)
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.
Author : Stefano Galluccio
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (129 download)
Download or read book Implied Calibration and Moments Asymptotics in Stochastic Volatility Jump Diffusion Models written by Stefano Galluccio and published by . This book was released on 2008 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine-quadratic class for the purpose of over-the-counter option pricing and risk-management. In particular, we aim at calibrating a stochastic volatility jump diffusion model to the whole market implied volatility surface at any given time. We study the asymptotic behaviour of the moments of the underlying distribution and use this information to introduce and implement our calibration algorithm. We numerically show that the proposed approach is both statistically stable and accurate.
Author : Pierre Henry-Labordere
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (129 download)
Download or read book A General Asymptotic Implied Volatility for Stochastic Volatility Models written by Pierre Henry-Labordere and published by . This book was released on 2005 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive a general asymptotic implied volatility at the first-order for any stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed with an Abelian connection. This formula is particularly useful for the calibration procedure. As an application, we obtain an asymptotic smile for a SABR model with a mean-reversion term, called lambda-SABR, corresponding in our geometric framework to the Poincare hyperbolic plane. When the lambda-SABR model degenerates into the SABR-model, we show that our asymptotic implied volatility is a better approximation than the classical Hagan-al expression. Furthermore, in order to show the strength of this geometric framework, we give an exact solution of the SABR model with beta=0 or 1. In a next paper, we will show how our method can be applied in other contexts such as the derivation of an asymptotic implied volatility for a Libor market model with a stochastic volatility.
Author : David Nicolay
Publisher : Springer
ISBN 13 : 1447165063
Total Pages : 503 pages
Book Rating : 4.4/5 (471 download)
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.
Author : Peter K. Friz
Publisher : Springer
ISBN 13 : 3319116053
Total Pages : 590 pages
Book Rating : 4.3/5 (191 download)
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.
Author : Ali M. E. Abdelrahman
Publisher :
ISBN 13 : 9788791927942
Total Pages : pages
Book Rating : 4.9/5 (279 download)
Download or read book Asymptotic Theory for the Sample Autocorrelation and the Extremes of Stochastic Volatility Models written by Ali M. E. Abdelrahman and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Geert Dhaene
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (249 download)
Download or read book Asymptotic Results for GMM Estimators of Stochastic Volatility Models written by Geert Dhaene and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (129 download)
Download or read book The Memory of Stochastic Volatility Models written by and published by . This book was released on 2008 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autovariances of time series generated by nonlinear transformation of Gaussian latent variates, and nonlinear functions of these, with special reference to long memory stochastic volatility models, serving to identify the roles played by the underlying Gaussian processes and the nonlinear transformation. Implications for simple stochastic volatility models are examined in detail, with numerical and Monte Carlo calculations, and applications to cyclic behaviour, cross-sectional and temporal aggregation, and multivariate models are discussed.
Author : Antoine Jacquier
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (93 download)
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 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jian Yang
Publisher :
ISBN 13 : 9780542777660
Total Pages : 0 pages
Book Rating : 4.7/5 (776 download)
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:
Author : Jaya P. N. Bishwal
Publisher : Springer Nature
ISBN 13 : 3031038614
Total Pages : 634 pages
Book Rating : 4.0/5 (31 download)
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
