Volatility Dynamics for a Single Underlying: Foundations

David Nicolay ()

Chapter Chapter 2 in Asymptotic Chaos Expansions in Finance, 2014, pp 23-116 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-1-4471-6506-4_2

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DOI: 10.1007/978-1-4471-6506-4_2

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