Large Deviations and Asymptotic Methods in Finance

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.

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