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Uncertain Volatility Models — Theory and Application

  • Robert Buff

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Introduction

    1. Robert Buff
      Pages 1-8
  3. Computational Finance: Theory

    1. Front Matter
      Pages 9-9
    2. Robert Buff
      Pages 11-13
    3. Robert Buff
      Pages 15-32
  4. Algorithms for Uncertain Volatility Models

    1. Front Matter
      Pages 45-45
    2. Robert Buff
      Pages 47-55
    3. Robert Buff
      Pages 57-60
    4. Robert Buff
      Pages 61-75
    5. Robert Buff
      Pages 77-122
    6. Robert Buff
      Pages 123-140
  5. Object-Oriented Implementation

    1. Front Matter
      Pages 141-141
    2. Robert Buff
      Pages 143-144
    3. Robert Buff
      Pages 145-184
    4. Robert Buff
      Pages 185-194
    5. Robert Buff
      Pages 197-202
    6. Robert Buff
      Pages 203-226
    7. Robert Buff
      Pages 227-232
  6. Back Matter
    Pages 233-243

About this book

Introduction

This book introduces Uncertain Volatility Models in mathematical finance. Uncertain Volatility Models evaluate option portfolios under worst- and best-case scenarios when the volatility coefficient of the pricing model cannot be determined exactly. The user defines subjective volatility constraints; within those constraints, extremal prices are computed. This book studies two types of constraints: volatility bands with upper and lower bounds, and shock scenarios with short periods of extreme volatility, but unknown timing. Uncertain Volatility Models are nonlinear. Worst- and best-case scenarios applied to isolated option positions do not always lead to the same extremal volatility. When applied to an options portfolio, a diversification effect reduces the overall exposure to volatility fluctuations within the subjective constraints. This book explores algorithmic issues that arise due to nonlinearity. Because Uncertain Volatility Models must be applied to option portfolios as a whole, they are difficult to implement on a computer if the portfolio contains barrier or American options. This book is for graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options.

Keywords

Mathematica Uncertain volatility models algorithms arbitrage pricing theory computational finance mathematical finance

Authors and affiliations

  • Robert Buff
    • 1
  1. 1.Goldman Sachs & Co.New YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-56323-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42657-8
  • Online ISBN 978-3-642-56323-2
  • Series Print ISSN 1616-0533
  • Buy this book on publisher's site