Articlebronze2009

Asymptotics of Implied Volatility far from Maturity

63 citations0/0 files storedJournal of Applied Probability

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

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.

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References

1998The Variance Gamma Process and Option Pricing 2003Affine processes and applications in finance 2000Derivatives in Financial Markets with Stochastic Volatility 2003The Finite Moment Log Stable Process and Option Pricing 2000Introduction and Summary of Results (Excerpt)2000The Term Structure of Implied Volatility 2005Local martingales, bubbles and option prices 2010MOMENT EXPLOSIONS AND LONG-TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS

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2011Asymptotics of Implied Volatility to Arbitrary Order 2020Implied Stochastic Volatility Models 2011Implied Volatility Surface: Construction Methodologies and Characteristics 2010Asymptotic formulae for implied volatility in the Heston model 2013A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS 2012Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models

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