Asymptotic Chaos Expansions in Finance

Theory and Practice

  • David┬áNicolay

Part of the Springer Finance book series (FINANCE)

Also part of the Springer Finance Lecture Notes book sub series (SFLN)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. David Nicolay
    Pages 1-20
  3. Single Underlying

    1. Front Matter
      Pages 21-21
    2. David Nicolay
      Pages 211-270
  4. Term Structures

    1. Front Matter
      Pages 271-271
    2. David Nicolay
      Pages 273-322
    3. David Nicolay
      Pages 323-366
    4. David Nicolay
      Pages 367-419
    5. David Nicolay
      Pages 421-428
  5. Back Matter
    Pages 429-491

About this book

Introduction

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.

Keywords

ACE Asymptotic Chaos Expansion Asymptotic Expansion Baseline Transfer Basket Option CEV Model ESMM Model Class Endogenous Driver Exogenous Driver FL-SV Model Freezing Approximation IATM Point Immediate Smile Implied Volatility Interest Rates Derivatives Ladder Effect Libor Market Model Local Volatility Model Calibration Moneyness Most Probable Path SABR Model Smile Descriptors Stochastic Implied Volatility Stochastic Instantaneous Volatility Stochastic Volatility Vega Hedging Wiener Chaos Zero Drift Condition

Authors and affiliations

  • David┬áNicolay
    • 1
  1. 1.LondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-6506-4
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-6505-7
  • Online ISBN 978-1-4471-6506-4
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • About this book