Large Deviations and Asymptotic Methods in Finance / edited by Peter K. Friz, Jim Gatheral, Archil Gulisashvili, Antoine Jacquier, Josef Teichmann.

Format:

Book

Contributor:

Friz, Peter K., Editor.

Gatheral, Jim., Editor.

Gulisashvili, Archil., Editor.

Jacquier, Antoine., Editor.

Teichmann, Josef., Editor.

Series:

Springer Proceedings in Mathematics & Statistics, 2194-1017 ; 110

Language:

English

Subjects (All):

Social sciences--Mathematics.

Probabilities.

Approximation theory.

Geometry, Differential.

Mathematics in Business, Economics and Finance.

Probability Theory.

Approximations and Expansions.

Differential Geometry.

Local Subjects:

Mathematics in Business, Economics and Finance.

Probability Theory.

Approximations and Expansions.

Differential Geometry.

Physical Description:

1 online resource (590 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.

Contents:

Hagan, Lesniewski, Woodward: Probability Distribution in the SABR Model of Stochastic Volatility

Paulot: Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

Henry-Labordere: Unifying the BGM and SABR Models: A Short Ride in Hyperbolic Geometry

Ben Arous, Laurence: Second Order Expansion for Implied Volatility in Two Factor Local-stochastic Volatility

Osajima: General Asymptotics of Wiener Functionals and Application to Implied Volatilities

Bayer, Laurence: Small-time asymptotics for the at-the-money implied volatility in a multi-dimensional local volatility model

Keller-Ressel, Teichmann: A Remark on Gatheral's 'Most-likely Path Approximation' of Implied Volatility

Gatheral, Wang: Implied volatility from local volatility: a path integral approach

Gerhold, Friz: Don't Stay Local - Extrapolation Analytics for Dupire's Local Volatility

Gulisashvili, Teichmann: Laplace Principle Expansions and Short Time Asymptotics for Affine Processes

Lorig, Pascucci, Pagliarani: Asymptotics for d-dimensional Levy-type Processes

Takahashi: An Asymptotic Expansion Approach in Finance

Baudoin, Ouyang: On small time asymptotics for rough differential equations driven by fractional Brownian motions

Lucic: On singularities in the Heston model.- Bayer, Friz, Laurence: On the probability density function of baskets

Conforti, De Marco, Deuschel: On small-noise equations with degenerate limiting system arising from volatility models

Pham: Long time asymptotic problems for optimal investment

Spiliopoulos: Systemic Risk and Default Clustering for Large Financial Systems

Jacod, Rosenbaum: Asymptotic Properties of a Volatility Estimator.

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

3-319-11605-3