On The Short Time Behavior Of The Implied Volatility For Jump Diffusion Models With Stochastic Volatility
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Author |
: Elisa Alós |
Publisher |
: |
Total Pages |
: |
Release |
: 2006 |
ISBN-10 |
: OCLC:803215674 |
ISBN-13 |
: |
Rating |
: 4/5 (74 Downloads) |
Synopsis On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility[ by : Elisa Alós
Author |
: Elisa Alós |
Publisher |
: |
Total Pages |
: |
Release |
: 2008 |
ISBN-10 |
: OCLC:804793379 |
ISBN-13 |
: |
Rating |
: 4/5 (79 Downloads) |
Synopsis A Hull and White Formula for a General Stochastic Volatility Jump-diffusion Model with Applications to the Study of the Short-time Behavior of the Implied Volatility by : Elisa Alós
Author |
: Mounir Zili |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 273 |
Release |
: 2011-09-24 |
ISBN-10 |
: 9783642223686 |
ISBN-13 |
: 3642223680 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Stochastic Differential Equations and Processes by : Mounir Zili
Selected papers submitted by participants of the international Conference “Stochastic Analysis and Applied Probability 2010” ( www.saap2010.org ) make up the basis of this volume. The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the “Applied Mathematics & Mathematical Physics” research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili. The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few. As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic numerical and theoretical analysis and statistics, as well as for graduate students. To make it more complete and accessible for graduate students, practitioners and researchers, the editors Mounir Zili and Daria Filatova have included a survey dedicated to the basic concepts of numerical analysis of the stochastic differential equations, written by Henri Schurz.
Author |
: Elisa Alos |
Publisher |
: CRC Press |
Total Pages |
: 350 |
Release |
: 2021-07-14 |
ISBN-10 |
: 9781000403510 |
ISBN-13 |
: 1000403513 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Malliavin Calculus in Finance by : Elisa Alos
Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.
Author |
: Stefano Galluccio |
Publisher |
: |
Total Pages |
: 32 |
Release |
: 2008 |
ISBN-10 |
: OCLC:1290312920 |
ISBN-13 |
: |
Rating |
: 4/5 (20 Downloads) |
Synopsis Implied Calibration and Moments Asymptotics in Stochastic Volatility Jump Diffusion Models by : Stefano Galluccio
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 |
: Christian Bayer |
Publisher |
: SIAM |
Total Pages |
: 292 |
Release |
: 2023-12-18 |
ISBN-10 |
: 9781611977783 |
ISBN-13 |
: 1611977789 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Rough Volatility by : Christian Bayer
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.
Author |
: Alexey Medvedev |
Publisher |
: |
Total Pages |
: 37 |
Release |
: 2006 |
ISBN-10 |
: OCLC:716913610 |
ISBN-13 |
: |
Rating |
: 4/5 (10 Downloads) |
Synopsis Approximation and Calibration of Short-term Implied Volatilities Under Jump-diffusion Stochastic Volatility by : Alexey Medvedev
Author |
: Hansjörg Albrecher |
Publisher |
: Walter de Gruyter |
Total Pages |
: 465 |
Release |
: 2009 |
ISBN-10 |
: 9783110213133 |
ISBN-13 |
: 3110213133 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Advanced Financial Modelling by : Hansjörg Albrecher
Annotation This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a a ~Special Semester on Stochastics with Emphasis on Financea (TM) that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria
Author |
: Emanuel Derman |
Publisher |
: John Wiley & Sons |
Total Pages |
: 532 |
Release |
: 2016-08-15 |
ISBN-10 |
: 9781118959176 |
ISBN-13 |
: 1118959175 |
Rating |
: 4/5 (76 Downloads) |
Synopsis The Volatility Smile by : Emanuel Derman
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.
Author |
: M'hamed Eddahbi |
Publisher |
: Springer |
Total Pages |
: 228 |
Release |
: 2016-04-08 |
ISBN-10 |
: 9783319304175 |
ISBN-13 |
: 3319304178 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Statistical Methods and Applications in Insurance and Finance by : M'hamed Eddahbi
This book is the outcome of the CIMPA School on Statistical Methods and Applications in Insurance and Finance, held in Marrakech and Kelaat M'gouna (Morocco) in April 2013. It presents two lectures and seven refereed papers from the school, offering the reader important insights into key topics. The first of the lectures, by Frederic Viens, addresses risk management via hedging in discrete and continuous time, while the second, by Boualem Djehiche, reviews statistical estimation methods applied to life and disability insurance. The refereed papers offer diverse perspectives and extensive discussions on subjects including optimal control, financial modeling using stochastic differential equations, pricing and hedging of financial derivatives, and sensitivity analysis. Each chapter of the volume includes a comprehensive bibliography to promote further research.