Multiple subordinated modeling of asset returns

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

Research output: Contribution to journalArticlepeer-review


Subordination is an often used stochastic process in modeling asset prices. Subordinated Lévy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial time-clocks motivated by behavioral finance. To be consistent with dynamic asset pricing theory and option pricing, as suggested by behavioral finance, the investors view is considered by introducing an intrinsic time process which we refer to as a behavioral subordinator. The process is subordinated to the Brownian motion process in the well-known log-normal model, resulting in a new log-price process. The number of embedded subordinations results in a new parameter that must be estimated and this parameter is as important as the mean and variance of asset returns. We describe new distributions, demonstrating how they can be applied to modeling the tail behavior of stock market returns. We apply the proposed models to modeling S&P 500 returns, treating the CBOE Volatility Index as intrinsic time change and the CBOE Volatility-of-Volatility Index as the volatility subordinator. We find that these volatility indexes are not proper time-change subordinators in modeling the returns of the S&P 500.

MSC Codes 91G99

Original languageEnglish
JournalUnknown Journal
StatePublished - Jul 29 2019


  • Behavioral finance
  • Dynamic asset pricing models
  • Lévy-stable distribution
  • Normal-compound inverse Gaussian distribution
  • Variance-gamma-gamma distribution

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