Asymptotic Chaos Expansions in Finance

Theory and Practice

David Nicolay (Autor)

Buch | Softcover

491 Seiten

2014
Springer London Ltd (Verlag)
978-1-4471-6505-7 (ISBN)

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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.

David Nicolay received his Ph.D. degree in financial mathematics from Ecole Polytechnique, France. Currently he is a front office quantitative researcher for a financial institution in London. His research interests include the modelling of interest rates and hybrid derivatives, Monte-Carlo methods and asymptotic approaches.

Introduction.- Volatility dynamics for a single underlying: foundations.- Volatility dynamics for a single underlying: advanced methods.- Practical applications and testing.- Volatility dynamics in a term structure.- Implied Dynamics in the SV-HJM framework.- Implied Dynamics in the SV-LMM framework.- Conclusion.

Reihe/Serie	Springer Finance
Reihe/Serie	Springer Finance Lecture Notes
Zusatzinfo	26 Illustrations, color; 8 Illustrations, black and white; XXII, 491 p. 34 illus., 26 illus. in color.
Verlagsort	England
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	ACE • Asymptotic Chaos Expansion • asymptotic expansion • Baseline Transfer • Basket Option • CEV Model • Endogenous Driver • ESMM Model Class • 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
ISBN-10	1-4471-6505-5 / 1447165055
ISBN-13	978-1-4471-6505-7 / 9781447165057
Zustand	Neuware