Maturity cycles in implied volatility

Jean Pierre Fouque, George Papanicolaou, Ronnie Sircar, Knut Solna

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [8]. The time-variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. By extending the mathematical analysis to incorporate model parameters which are time-varying, we show this behaviour can be explained in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients.

Original languageEnglish (US)
Pages (from-to)451-477
Number of pages27
JournalFinance and Stochastics
Issue number4
StatePublished - Nov 2004

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


  • Asymptotic expansions
  • Fast mean-reverting stochastic volatility
  • Implied volatilities
  • Maturity cycles


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