Authors:
- Exposes some structural links, both static and dynamic, between classic stochastic instantaneous volatility models and the more recent stochastic implied volatility model class
- Provides a programmable methodology to compute the small-time asymptotics, at any order, of the smile associated to any regular stochastic volatility model
- Presents simple but powerful illustrations of the methodology, in particular some applications to Local Volatility models which expose the systematic bias of the 'most probable path' method
- Includes self-contained, high-order generic approximations for single-underlying SV models (such as Heston or SABR) to improve calibration and Vega-hedging
- Extends the ACE approach progressively, first to multi-dimensional frameworks and baskets, then to term structure models. In particular, derives the asymptotic smiles of generic SV-HJM and SV-LMM models
- 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 (8 chapters)
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Front Matter
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Term Structures
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Front Matter
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Back Matter
About this book
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
- partial differential equations
Authors and Affiliations
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London, United Kingdom
David Nicolay
About the author
Bibliographic Information
Book Title: Asymptotic Chaos Expansions in Finance
Book Subtitle: Theory and Practice
Authors: David Nicolay
Series Title: Springer Finance
DOI: https://doi.org/10.1007/978-1-4471-6506-4
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2014
Softcover ISBN: 978-1-4471-6505-7Published: 05 December 2014
eBook ISBN: 978-1-4471-6506-4Published: 25 November 2014
Series ISSN: 1616-0533
Series E-ISSN: 2195-0687
Edition Number: 1
Number of Pages: XXII, 491
Number of Illustrations: 8 b/w illustrations, 26 illustrations in colour
Topics: Partial Differential Equations, Quantitative Finance, Numerical Analysis, Mathematical Modeling and Industrial Mathematics, Probability Theory and Stochastic Processes