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Springer Proceedings in Mathematics & Statistics

Large Deviations and Asymptotic Methods in Finance

Editors: Friz, P.K., Gatheral, J., Gulisashvili, A., Jacquier, A., Teichmann, J. (Eds.)

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  • Is a unique comprehensive collection of asymptotic methods and mathematical tools that covers a wide range of topics
  • Provides interesting applications of large deviations, differential geometry, and stochastic analysis to practical financial problems
  • Presents cutting-edge resources for academics and practitioners in the field of volatility modelling, systemic risk, high frequency, pricing and calibration methods
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eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-319-11605-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 166,39 €
price for Spain (gross)
  • ISBN 978-3-319-11604-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-319-38512-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

Peter K. Friz is presently full professor at TU and WIAS Berlin. After studies in Vienna, Paris and Trinity College, Cambridge, he obtained his PhD under the supervision of
S.R.S. Varadhan at the Courant Institute of New York University. In 2003-04 he worked for Merrill Lynch, New York, before returning to academia where he then held a Readership at Cambridge University until his move to Berlin in 2009.  PKF has written numerous papers in the broad area of quantitative finance,  partial differential equations, stochastic analysis and two highly regarded books on applications of rough paths theory: "Multidimensional Stochastic Processes as  Rough Paths" (with N. Victoir, Cambridge University Press 2010), "A Course on Rough Paths, with an Introduction to Regularity Structures" (with M. Hairer, Springer 2014).

Jim Gatheral is professor of mathematics at Baruch College, CUNY, and primarily teaches courses in the Masters of Financial Engineering (MFE) program. Prior to this, he was a Managing Director at Bank of America Merrill Lynch, and also an adjunct professor at the Courant Institute of Mathematical Sciences, New York, where for many years he co-taught popular classes in the Masters Program of Mathematics in Finance. Prior to 2005 he headed the Equity Quantitative Analytics groups at Merrill Lynch. Over his long career in the financial markets, he has been involved at one time or other in all of the major derivative product areas as book runner, risk manager and quantitative analyst. Jim has a PhD in theoretical physics from Cambridge University. His research focus is on volatility modelling and modelling equity market microstructure for algorithmic trading. His best-selling book, The Volatility Surface: A Practitioner's Guide (Wiley 2006), is one of the standard references on the subject of volatility modelling.

Archil Gulisashvili received his Ph.D. and Doctor of Sciences degrees from Tbilisi State University, Georgia. Currently he is a Professor of Mathematics at Ohio University, USA. Prior to joining Ohio University, he has held visiting positions at Boston University, Cornell University and Howard University. His research interests include financial mathematics (stochastic volatility models, stock price densities, option pricing functions, smile asymptotics), and also Schrödinger semigroups, Feynman-Kac propagators and Fourier analysis.

Antoine Jacquier is a lecturer in the Department of Mathematics at Imperial College London. His research interests include large deviations methods and asymptotic expansions for stochastic processes, and their applications to implied volatility modelling. He previously worked for AXA Investment Management and Societe Generale. Antoine graduated from ESSEC Business School and holds a Ph.D. in Mathematics from Imperial College London.

Josef Teichmann is a professor at ETH Zürich working on mathematical finance. After studying mathematics at the University of Graz, he pursued his PhD in functional analysis on Lie Groups at the University of Vienna. After working at the Vienna University of Technology, he completed his Habilitation there in 2002. Since June 2009 he has been a Professor at the Department of Mathematics at ETH Zürich. In 2005 he was awarded the Prize of the Austrian Mathematical Society and in 2006 the Start-Preis of the FWF.

Table of contents (20 chapters)

Table of contents (20 chapters)
  • Probability Distribution in the SABR Model of Stochastic Volatility

    Pages 1-35

    Hagan, Patrick (et al.)

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

    Pages 37-69

    Paulot, Louis

  • Unifying the BGM and SABR Models: A Short Ride in Hyperbolic Geometry

    Pages 71-88

    Henry-Labordère, Pierre

  • Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and Applications to the Dynamic $$\lambda $$-Sabr Model

    Pages 89-136

    Ben Arous, Gérard (et al.)

  • General Asymptotics of Wiener Functionals and Application to Implied Volatilities

    Pages 137-173

    Osajima, Yasufumi

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-319-11605-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 166,39 €
price for Spain (gross)
  • ISBN 978-3-319-11604-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-319-38512-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Large Deviations and Asymptotic Methods in Finance
Editors
  • Peter K. Friz
  • Jim Gatheral
  • Archil Gulisashvili
  • Antoine Jacquier
  • Josef Teichmann
Series Title
Springer Proceedings in Mathematics & Statistics
Series Volume
110
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-11605-1
DOI
10.1007/978-3-319-11605-1
Hardcover ISBN
978-3-319-11604-4
Softcover ISBN
978-3-319-38512-9
Series ISSN
2194-1009
Edition Number
1
Number of Pages
IX, 590
Number of Illustrations
12 b/w illustrations, 14 illustrations in colour
Topics