Asymptotic Chaos Expansions in Finance

Theory and Practice

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Asymptotic Chaos Expansions in Finance by David Nicolay, Springer London
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: David Nicolay ISBN: 9781447165064
Publisher: Springer London Publication: November 25, 2014
Imprint: Springer Language: English
Author: David Nicolay
ISBN: 9781447165064
Publisher: Springer London
Publication: November 25, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer London

Cover of the book Neonatal Tumours by David Nicolay
Cover of the book Digital Signal Processing in Power System Protection and Control by David Nicolay
Cover of the book Dynamic Business Process Formation for Instant Virtual Enterprises by David Nicolay
Cover of the book Complex Analysis by David Nicolay
Cover of the book Migratory Interactive Applications for Ubiquitous Environments by David Nicolay
Cover of the book Bone Implant Grafting by David Nicolay
Cover of the book Case Based Echocardiography by David Nicolay
Cover of the book Pediatric Critical Care Medicine by David Nicolay
Cover of the book Textbook of Real-Time Three Dimensional Echocardiography by David Nicolay
Cover of the book Fundamentals of Digital Manufacturing Science by David Nicolay
Cover of the book The Hand and the Brain by David Nicolay
Cover of the book Requirements Engineering by David Nicolay
Cover of the book Automation in Warehouse Development by David Nicolay
Cover of the book Hacking Europe by David Nicolay
Cover of the book Beyond Deep Blue by David Nicolay
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy