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Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation

In: Recent Advances in Applied Probability

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  • Roger W. Lee

    (Stanford University, Department of Mathematics
    NYU, Courant Institute of Mathematical Sciences)

Abstract

Given the price of a call or put option, the Black-Scholes implied volatility is the unique volatility parameter for which the Black-Scholes formula recovers the option price. This article surveys research activity relating to three theoretical questions: First, does implied volatility admit a probabilistic interpretation? Second, how does implied volatility behave as a function of strike and expiry? Here one seeks to characterize the shapes of the implied volatility skew (or smile) and term structure, which together constitute what can be termed the statics of the implied volatility surface. Third, how does implied volatility evolve as time rolls forward? Here one seeks to characterize the dynamics of implied volatility.

Suggested Citation

  • Roger W. Lee, 2005. "Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation," Springer Books, in: Ricardo Baeza-Yates & Joseph Glaz & Henryk Gzyl & Jürgen Hüsler & José Luis Palacios (ed.), Recent Advances in Applied Probability, pages 241-268, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-23394-9_11
    DOI: 10.1007/0-387-23394-6_11
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