Approximation And Calibration Of Short Term Implied Volatilities Under Jump Diffusion Stochastic Volatility
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| Author | : David Nicolay |
| Publisher | : Springer |
| Total Pages | : 503 |
| Release | : 2014-11-25 |
| Genre | : Mathematics |
| ISBN | : 1447165063 |
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 |
| Total Pages | : 590 |
| Release | : 2015-06-16 |
| Genre | : Mathematics |
| ISBN | : 3319116053 |
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 | : Elisa Alos |
| Publisher | : CRC Press |
| Total Pages | : 350 |
| Release | : 2021-07-14 |
| Genre | : Mathematics |
| ISBN | : 1000403513 |
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 | : John B. Guerard, Jr. |
| Publisher | : Springer |
| Total Pages | : 480 |
| Release | : 2016-09-23 |
| Genre | : Business & Economics |
| ISBN | : 3319339761 |
This volume, inspired by and dedicated to the work of pioneering investment analyst, Jack Treynor, addresses the issues of portfolio risk and return and how investment portfolios are measured. In a career spanning over fifty years, the primary questions addressed by Jack Treynor were: Is there an observable risk-return trade-off? How can stock selection models be integrated with risk models to enhance client returns? Do managed portfolios earn positive, and statistically significant, excess returns and can mutual fund managers time the market? Since the publication of a pair of seminal Harvard Business Review articles in the mid-1960’s, Jack Treynor has developed thinking that has greatly influenced security selection, portfolio construction and measurement, and market efficiency. Key publications addressed such topics as the Capital Asset Pricing Model and stock selection modeling and integration with risk models. Treynor also served as editor of the Financial Analysts Journal, through which he wrote many columns across a wide spectrum of topics. This volume showcases original essays by leading researchers and practitioners exploring the topics that have interested Treynor while applying the most current methodologies. Such topics include the origins of portfolio theory, market timing, and portfolio construction in equity markets. The result not only reinforces Treynor’s lasting contributions to the field but suggests new areas for research and analysis.
| Author | : |
| Publisher | : |
| Total Pages | : 486 |
| Release | : 2008 |
| Genre | : Finance |
| ISBN | : |
| Author | : Peter Tankov |
| Publisher | : CRC Press |
| Total Pages | : 552 |
| Release | : 2003-12-30 |
| Genre | : Business & Economics |
| ISBN | : 1135437947 |
WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
| Author | : Ole E Barndorff-Nielsen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 414 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461201977 |
A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.
| Author | : Ricardo Baeza-Yates |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 497 |
| Release | : 2006-02-28 |
| Genre | : Mathematics |
| ISBN | : 0387233946 |
Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.
| Author | : Fabrice D. Rouah |
| Publisher | : John Wiley & Sons |
| Total Pages | : 437 |
| Release | : 2013-08-01 |
| Genre | : Business & Economics |
| ISBN | : 1118695178 |
Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
| Author | : Pierre Henry-Labordere |
| Publisher | : CRC Press |
| Total Pages | : 403 |
| Release | : 2008-09-22 |
| Genre | : Business & Economics |
| ISBN | : 1420087002 |
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th
