LEADER 04395nam 22007335 450 001 9910299969103321 005 20230810155905.0 010 $a1-4471-6506-3 024 7 $a10.1007/978-1-4471-6506-4 035 $a(CKB)3710000000291402 035 $a(EBL)1967807 035 $a(OCoLC)897115916 035 $a(SSID)ssj0001386348 035 $a(PQKBManifestationID)11766751 035 $a(PQKBTitleCode)TC0001386348 035 $a(PQKBWorkID)11349401 035 $a(PQKB)10162698 035 $a(MiAaPQ)EBC1967807 035 $a(DE-He213)978-1-4471-6506-4 035 $a(PPN)183096266 035 $a(EXLCZ)993710000000291402 100 $a20141125d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic Chaos Expansions in Finance $eTheory and Practice /$fby David Nicolay 205 $a1st ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (503 p.) 225 1 $aSpringer Finance Lecture Notes,$x2524-6828 300 $aDescription based upon print version of record. 311 $a1-4471-6505-5 320 $aIncludes bibliographical references and index at the end of each chapters. 327 $aIntroduction -- 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. 330 $aStochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution. 410 0$aSpringer Finance Lecture Notes,$x2524-6828 606 $aDifferential equations 606 $aSocial sciences$xMathematics 606 $aNumerical analysis 606 $aMathematical models 606 $aProbabilities 606 $aDifferential Equations 606 $aMathematics in Business, Economics and Finance 606 $aNumerical Analysis 606 $aMathematical Modeling and Industrial Mathematics 606 $aProbability Theory 615 0$aDifferential equations. 615 0$aSocial sciences$xMathematics. 615 0$aNumerical analysis. 615 0$aMathematical models. 615 0$aProbabilities. 615 14$aDifferential Equations. 615 24$aMathematics in Business, Economics and Finance. 615 24$aNumerical Analysis. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aProbability Theory. 676 $a330.0151 700 $aNicolay$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721757 906 $aBOOK 912 $a9910299969103321 996 $aAsymptotic chaos expansions in finance$91410651 997 $aUNINA