Multiple subordinated modeling of asset returns: Implications for option pricing

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.