Asymptotic Chaos Expansions in Finance: Theory and Practice

by David Nicolay

Overview

Shastic 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 sk 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 shastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in shastic 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.

Product Details

ISBN-13:	9781447165057
Publisher:	Springer London
Publication date:	12/05/2014
Series:	Springer Finance
Edition description:	2014
Pages:	491
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

About the Author

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.

Table of Contents

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.