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Titlebook: Asymptotic Chaos Expansions in Finance; Theory and Practice David Nicolay Book 2014 Springer-Verlag London 2014 ACE.Asymptotic Chaos Expans

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发表于 2025-3-21 19:14:52 | 显示全部楼层 |阅读模式
期刊全称Asymptotic Chaos Expansions in Finance
期刊简称Theory and Practice
影响因子2023David Nicolay
视频video
发行地址Exposes some structural links, both static and dynamic, between classic stochastic instantaneous volatility models and the more recent stochastic implied volatility model class.Provides a programmable
学科分类Springer Finance
图书封面Titlebook: Asymptotic Chaos Expansions in Finance; Theory and Practice David Nicolay Book 2014 Springer-Verlag London 2014 ACE.Asymptotic Chaos Expans
影响因子.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
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Volatility Dynamics for a Single Underlying: Foundationship between . (SInsV) and . (SImpV) models, in the simple case of a single underlying, and when the endogenous driver is scalar. We discuss both the inverse (or recovery) and the direct problem, initially limiting the asymptotic expansion to its lowest order, which we call the .. We illustrate these
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Volatility Dynamics for a Single Underlying: Advanced Methodsctical and/or some mathematical interest. First we describe the generic ACE methodology solving the direct problem at an arbitrary order. We then apply this algorithm to compute meaningful IATM differentials, all located within the second and third layers, which we can then exploit and interpret. Ne
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Implied Dynamics in the SV-LMM FrameworkStochastic Volatility Libor Market Model (SV-LMM). As in Chap. ., our main focus is to solve the direct problem (generating the smile’s shape and dynamics from the model specification) up to the first layer (which includes the smile’s curvature and slope). We target some of the most liquid option ty
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Conclusionplicit and non-arbitrable connection between some of the SV model classes, which are capable of describing the joint dynamics of an underlying and of its associated European options. That connection could be approximate, provided that its precision was known and if possible controllable. We also dem
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978-1-4471-6505-7Springer-Verlag London 2014
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