Asymptotic Analysis of Implied Volatility

Archil Gulisashvili
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Archil Gulisashvili: Ohio University

Chapter Chapter 9 in Analytically Tractable Stochastic Stock Price Models, 2012, pp 243-272 from Springer

Abstract: Abstract The implied volatility was first introduced by H.A. Latané and R.J. Rendleman under the name “the implied standard deviation”. Latané and Rendleman studied standard deviations of asset returns, which are implied in actual call option prices when investors price options according to the Black-Scholes model. Chapter 9 mainly is concerned with the asymptotics of the implied volatility at extreme strikes. It presents sharp model-free asymptotic formulas for the implied volatility established by the author and the higher order extensions of these formulas found by K. Gao and R. Lee. The chapter also provides a characterization of implied volatility models free of static arbitrage, and discusses certain symmetries hidden in stochastic asset price models. These symmetries can be used to analyze the asymptotic behavior of the implied volatility at small strikes knowing how the volatility behaves at large strikes.

Keywords: Asymptotic Formula; Implied Volatility; Symmetric Model; Static Arbitrage; Strike Price (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-31214-4_9

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DOI: 10.1007/978-3-642-31214-4_9

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