Multiple subordinated modeling of asset returns: Implications for option pricing

Abootaleb Shirvani, Svetlozar T. Rachev, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review


Motivated by behavioral finance, we introduce multiple embedded financial time clocks. Consistent with asset pricing theory in analyzing equity returns, the investors’ view is considered by introducing a behavioral subordinator. Subordinating to the Brownian motion process in the log-normal model results in a new log-price process whose parameter is as important as the mean and variance. We describe new distributions, demonstrating their use to model tail behavior. The models are applied to S&P 500 returns, treating the Chicago Board Options Exchange (CBOE) volatility index (VIX) as intrinsic-time change and CBOE Volatility-of-Volatility Index as the volatility subordinator. We find these volatility indexes fail as time-change subordinators. We employ a double subordinator model to explain the equity premium puzzle and the excess volatility puzzle. The results indicate the puzzles can be explained by fitting a double subordinator model to the historical data.

Original languageEnglish
Pages (from-to)290-319
Number of pages30
JournalEconometric Reviews
Issue number3
StatePublished - 2021


  • Behavioral finance
  • Lévy-stable distribution
  • dynamic asset pricing models
  • normal-compound inverse Gaussian distribution
  • variance-gamma-gamma distribution


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