Multiple Subordinated Modeling of Asset Returns

TL;DR

This paper introduces a novel multiple subordination framework for asset return modeling, incorporating behavioral finance insights through intrinsic time processes, and demonstrates its application to S&P 500 data with specific volatility indexes.

Contribution

It develops a new theory of multiple embedded financial time-clocks, including behavioral subordinators, and applies it to model stock returns with empirical analysis.

Findings

Volatility indexes like VIX are not suitable as time-change subordinators.

New distributions are proposed for modeling tail behavior of returns.

Application to S&P 500 shows the model's relevance and limitations.

Abstract

Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy 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.