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Asymptotics of Implied Volatility far from Maturity

Part of: Limit theorems Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Michael R. Tehranchi
Michael R. Tehranchi*
Affiliation:
University of Cambridge
*
∗Postal address: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: m.tehranchi@statslab.cam.ac.uk
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Abstract

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This note explores the behaviour of the implied volatility of a European call option far from maturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.

Keywords

Implied volatilitylarge deviationssaddle-point approximation

MSC classification

Secondary: 91B70: Stochastic models 60F10: Large deviations
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 629 - 650
Copyright
Copyright © Applied Probability Trust 2009 

References

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