04395nam 22007335 450 991029996910332120230810155905.01-4471-6506-310.1007/978-1-4471-6506-4(CKB)3710000000291402(EBL)1967807(OCoLC)897115916(SSID)ssj0001386348(PQKBManifestationID)11766751(PQKBTitleCode)TC0001386348(PQKBWorkID)11349401(PQKB)10162698(MiAaPQ)EBC1967807(DE-He213)978-1-4471-6506-4(PPN)183096266(EXLCZ)99371000000029140220141125d2014 u| 0engur|n|---|||||txtccrAsymptotic Chaos Expansions in Finance Theory and Practice /by David Nicolay1st ed. 2014.London :Springer London :Imprint: Springer,2014.1 online resource (503 p.)Springer Finance Lecture Notes,2524-6828Description based upon print version of record.1-4471-6505-5 Includes bibliographical references and index at the end of each chapters.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.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.Springer Finance Lecture Notes,2524-6828Differential equationsSocial sciencesMathematicsNumerical analysisMathematical modelsProbabilitiesDifferential EquationsMathematics in Business, Economics and FinanceNumerical AnalysisMathematical Modeling and Industrial MathematicsProbability TheoryDifferential equations.Social sciencesMathematics.Numerical analysis.Mathematical models.Probabilities.Differential Equations.Mathematics in Business, Economics and Finance.Numerical Analysis.Mathematical Modeling and Industrial Mathematics.Probability Theory.330.0151Nicolay Davidauthttp://id.loc.gov/vocabulary/relators/aut721757BOOK9910299969103321Asymptotic chaos expansions in finance1410651UNINA