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Fitting Local Volatility Analytic And Numerical Approaches In Black Scholes And Local Variance Gamma Models
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Book Synopsis Fitting Local Volatility: Analytic And Numerical Approaches In Black-scholes And Local Variance Gamma Models by : Andrey Itkin
Download or read book Fitting Local Volatility: Analytic And Numerical Approaches In Black-scholes And Local Variance Gamma Models written by Andrey Itkin and published by World Scientific. This book was released on 2020-01-22 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
Book Synopsis Fitting Local Volatility by : Andrey Itkin
Download or read book Fitting Local Volatility written by Andrey Itkin and published by . This book was released on 2020 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Integral Transforms In Mathematical Finance by : Andrey Itkin
Download or read book Generalized Integral Transforms In Mathematical Finance written by Andrey Itkin and published by World Scientific. This book was released on 2021-10-12 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.
Book Synopsis Volatility Surface and Term Structure by : Kin Keung Lai
Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.
Book Synopsis Option Pricing Models and Volatility Using Excel-VBA by : Fabrice D. Rouah
Download or read book Option Pricing Models and Volatility Using Excel-VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2012-06-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland
Book Synopsis Derivatives in Financial Markets with Stochastic Volatility by : Jean-Pierre Fouque
Download or read book Derivatives in Financial Markets with Stochastic Volatility written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2000-07-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
Book Synopsis Applied Conic Finance by : Dilip Madan
Download or read book Applied Conic Finance written by Dilip Madan and published by Cambridge University Press. This book was released on 2016-10-13 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the brand new theory of conic finance, also referred to as the two-price theory, which determines bid and ask prices in a consistent and fundamentally motivated manner. Whilst theories of one price classically eliminate all risk, the concept of acceptable risks is critical to the foundations of the two-price theory which sees risk elimination as typically unattainable in a modern financial economy. Practical examples and case studies provide the reader with a comprehensive introduction to the fundamentals of the theory, a variety of advanced quantitative models, and numerous real-world applications, including portfolio theory, option positioning, hedging, and trading contexts. This book offers a quantitative and practical approach for readers familiar with the basics of mathematical finance to allow them to boldly go where no quant has gone before.
Book Synopsis An Introduction to Financial Option Valuation by : Desmond J. Higham
Download or read book An Introduction to Financial Option Valuation written by Desmond J. Higham and published by Cambridge University Press. This book was released on 2004-04-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
Book Synopsis Mathematical Methods for Foreign Exchange by : Alexander Lipton
Download or read book Mathematical Methods for Foreign Exchange written by Alexander Lipton and published by World Scientific. This book was released on 2001 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book presents a systematic and practically oriented approach to mathematical modeling in finance, particularly in the foreign exchange context. It describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic, and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results. The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.
Book Synopsis The Black-Scholes Model by : Marek Capiński
Download or read book The Black-Scholes Model written by Marek Capiński and published by Cambridge University Press. This book was released on 2012-09-13 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master the essential mathematical tools required for option pricing within the context of a specific, yet fundamental, pricing model.
Book Synopsis The Heston Model and its Extensions in Matlab and C# by : Fabrice D. Rouah
Download or read book The Heston Model and its Extensions in Matlab and C# written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Mathematical Finance by : Michael C. Fu
Download or read book Advances in Mathematical Finance written by Michael C. Fu and published by Springer Science & Business Media. This book was released on 2007-06-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
Book Synopsis The Complete Guide to Option Pricing Formulas by : Espen Gaarder Haug
Download or read book The Complete Guide to Option Pricing Formulas written by Espen Gaarder Haug and published by Professional Finance & Investment. This book was released on 2007-01-08 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains ... "all pricing formulas, with VBA code and ready-to-use Excel spreadsheets and 3D charts for Greeks (or Option Sensitivities)."--Jacket.
Book Synopsis Frontiers in Quantitative Finance by : Rama Cont
Download or read book Frontiers in Quantitative Finance written by Rama Cont and published by John Wiley & Sons. This book was released on 2009-03-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Petit D'euner de la Finance–which author Rama Cont has been co-organizing in Paris since 1998–is a well-known quantitative finance seminar that has progressively become a platform for the exchange of ideas between the academic and practitioner communities in quantitative finance. Frontiers in Quantitative Finance is a selection of recent presentations in the Petit D'euner de la Finance. In this book, leading quants and academic researchers cover the most important emerging issues in quantitative finance and focus on portfolio credit risk and volatility modeling.
Book Synopsis Applied Quantitative Finance by : Wolfgang Karl Härdle
Download or read book Applied Quantitative Finance written by Wolfgang Karl Härdle and published by Springer. This book was released on 2017-08-02 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides practical solutions and introduces recent theoretical developments in risk management, pricing of credit derivatives, quantification of volatility and copula modeling. This third edition is devoted to modern risk analysis based on quantitative methods and textual analytics to meet the current challenges in banking and finance. It includes 14 new contributions and presents a comprehensive, state-of-the-art treatment of cutting-edge methods and topics, such as collateralized debt obligations, the high-frequency analysis of market liquidity, and realized volatility. The book is divided into three parts: Part 1 revisits important market risk issues, while Part 2 introduces novel concepts in credit risk and its management along with updated quantitative methods. The third part discusses the dynamics of risk management and includes risk analysis of energy markets and for cryptocurrencies. Digital assets, such as blockchain-based currencies, have become popular b ut are theoretically challenging when based on conventional methods. Among others, it introduces a modern text-mining method called dynamic topic modeling in detail and applies it to the message board of Bitcoins. The unique synthesis of theory and practice supported by computational tools is reflected not only in the selection of topics, but also in the fine balance of scientific contributions on practical implementation and theoretical concepts. This link between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners convenient access to new techniques in quantitative finance. Hence the book will appeal both to researchers, including master and PhD students, and practitioners, such as financial engineers. The results presented in the book are fully reproducible and all quantlets needed for calculations are provided on an accompanying website. The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allows readers to reproduce the tables, pictures and calculations inside this Springer book.
Book Synopsis Financial Modelling with Jump Processes by : Peter Tankov
Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
