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Volatility Dynamics for a Single Underlying: Foundations

  • David NicolayEmail author
Chapter
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Part of the Springer Finance book series (FINANCE)

Abstract

In this first and fundamental chapter we lay out the core principles of the Asymptotic Chaos Expansion (ACE) methodology. We investigate the relationship between stochastic instantaneous volatility (SInsV) and stochastic implied volatility (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 first layer. We illustrate these asymptotic results first with the local volatility (LV) class, and then with a comprehensive extension to stochastic volatility (SV) dynamics.

Keywords

Implied Volatility Stochastic Volatility Model Local Volatility Call Price Implied Volatility Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.LondonUK

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