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Uncertain Volatility Models

Theory and Application

  • Book
  • © 2002

Overview

Authors:
  1. Robert Buff

    1. Goldman Sachs & Co., New York, USA

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  • No other book does this
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Finance (FINANCE)

Part of the book sub series: Springer Finance Lecture Notes (SFLN)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Robert Buff
      Pages 1-8

  3. Computational Finance: Theory

    1. Front Matter

      Pages 9-9
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    2. Notation and Basic Definitions

      • Robert Buff
      Pages 11-13

    3. Continuous Time Finance

      • Robert Buff
      Pages 15-32

    4. Scenario-Based Evaluation and Uncertainty

      • Robert Buff
      Pages 33-43

  4. Algorithms for Uncertain Volatility Models

    1. Front Matter

      Pages 45-45
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    2. A Lattice Framework

      • Robert Buff
      Pages 47-55

    3. Algorithms for Vanilla Options

      • Robert Buff
      Pages 57-60

    4. Algorithms for Barrier Options

      • Robert Buff
      Pages 61-75

    5. Algorithms for American Options

      • Robert Buff
      Pages 77-122

    6. Exotic Volatility Scenarios

      • Robert Buff
      Pages 123-140

  5. Object-Oriented Implementation

    1. Front Matter

      Pages 141-141
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    2. The Architecture of Mtg

      • Robert Buff
      Pages 143-144

    3. The Class Hierarchy of MtgLib—External

      • Robert Buff
      Pages 145-184

    4. The Class Hierarchy of MtgLib—Internal

      • Robert Buff
      Pages 185-194

    5. Extensions for Monte-Carlo Pricing and Calibration

      • Robert Buff
      Pages 195-196

    6. The Network Application MtgClt / MtgSvr

      • Robert Buff
      Pages 197-202

    7. The Scripting Language MtgScript

      • Robert Buff
      Pages 203-226

    8. Mathematica Extensions

      • Robert Buff
      Pages 227-232
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Keywords

About this book

Many introductory books on mathematical finance also outline some com­ puter algorithms. My goal is to contribute a closer look at algorithmic issues that arise from complex forms of the underlying pricing models-issues many practitioners need to solve sooner or later in their careers. This book takes such a close look at uncertain volatility models, an exten­ sion of Black-Scholes theory.It discusses applications to exotic option portfo­ lios with barriers and early exercise features. It describes an object-oriented C++ solution, included in source code on the accompanying CD. Practitioners and students who need to build analytic software libraries may benefit from reading this book and studying the software. The book focuses on a family of mathematical models, while in the field one encounters greater variation in instrument properties. In both cases mathematical and financial knowledge must be complemented by good programming skills to produce the best system. Analytic software needs design-a central message of the later chapters of this book. This book has come out of my Ph.D. thesis. I am very grateful to my academic advisor, Marco Avellaneda of New York University, who taught me mathematical finance and uncertain volatility. Computational finance be­ came exciting for me because Marco encouraged an algorithmic approach to uncertain volatility. I thank Afshin Bayrooti, Vladimir Finkelstein, and Antonio Paras for giving valuable feedback. Antonio is the co-inventor of the original uncertain volatility model, A-UVM. Richard Holmes has found a crucial bug in an early implementation of the software.

Reviews

From the reviews:

MATHEMATICAL REVIEWS

"The book bridges theory and real-world problems in a clear and pragmatic fashion. It can be useful both for academics and professionals in the financial community."

"This book, which comes out of the author’s Ph.D. thesis, introduces uncertain volatility models. … The formal results are illustrated by many empirical examples. … The book bridges theory and real-world problems in a clear and pragmatic fashion. It can be useful both for academics and for professionals in the financial community." (Damir Filipovic, Mathematical Reviews, 2003 i)

"The book is devoted to the study of uncertain volatility models that evaluate option portfolios … . The author travels in this book the entire road from innovative mathematical finance to a working software system … . Practitioners and students who need to build analytic software libraries may benefit from reading this book … . This book is also for graduate students and researchers who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options." (Anatoliy Swishchuk, Zentralblatt MATH, Vol. 1004 (4), 2003)

Authors and Affiliations

  • Goldman Sachs & Co., New York, USA

    Robert Buff

Bibliographic Information

  • Book Title: Uncertain Volatility Models

  • Book Subtitle: Theory and Application

  • Authors: Robert Buff

  • Series Title: Springer Finance

  • DOI: https://doi.org/10.1007/978-3-642-56323-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-42657-8Published: 10 April 2002

  • eBook ISBN: 978-3-642-56323-2Published: 06 December 2012

  • Series ISSN: 1616-0533

  • Series E-ISSN: 2195-0687

  • Edition Number: 1

  • Number of Pages: XII, 244

  • Topics: Quantitative Finance

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