Co-existence of trend and value in financial markets: Estimating an extended Chiarella model

Abstract

Trend and Value are pervasive anomalies, common to all financial markets. We address the problem of their co-existence and interaction within the framework of Heterogeneous Agent Based Models (HABM). More specifically, we extend the Chiarella (1992) model by adding noise traders and a non-linear demand of fundamentalists. We use Bayesian filtering techniques to calibrate the model on time series of prices across a variety of asset classes since 1800. The fundamental value is an output of the calibration, and does not require the use of an external pricing model. Our extended model reproduces many empirical observations, including the non-monotonic relation between past trends and future returns. The destabilizing activity of trend-followers leads to a qualitative change of mispricing distribution, from unimodal to bimodal, meaning that some markets tend to be over-(or under-) valued for long periods of time.

Can heterogeneous agent models explain the alleged mispricing of the S&P 500?

“…Our approach in this section is very close to that of Majewski et al (2020) who also estimate nonlinear functions up to cubic order for chartists' and fundamentalists' excess demand functions. While their setting is different (they use a state-space formalization of an extended version of Chiarella's model), the results are very close in their overall support of the relevance of higher-order terms.…”

“…This model has also been estimated by Majewski et al (2020) who consider an extended version with nonlinearities in both the chartists' and fundamentalists' excess demand functions, and the fundamental value being treated as a hidden variable in a state space framework.…”

“…In recent literature, there is one other contribution with a closely related approach: Majewski et al (2020) estimate an extended version of the model of Chiarella (1992), and show that the estimated parameters indeed give rise to bi-modality for certain financial data (e.g, the US stock market). Majewski et al, however, do not compare the performance of this model with other candidate models, and they use a statespace approach to identify the fundamental value as a hidden variable (while here we use Shiller's ex-post findamental value as a benchmark).…”

Bayesian estimation and likelihood-based comparison of agent-based volatility models

“…This not only makes the unobserved latent states of the model unidentifiable, but also reveals that our understanding of agent-based models and their generated time series dynamics is far from complete. In particular, we cannot use the model in order to unambiguously uncover the fundamental price as in Majewski et al (2018) where the Kalman filter computes a uni-modal posterior approximation. Furthermore, the herding parameters are hard to interpret as they act differently in different modes.…”

“…Estimating agent-based models in this fashion is challenging as their dynamics are often highly nonlinear. Yet recently, sequential Monte Carlo methods (Lux 2018) and the unscented Kalman filter (Majewski et al 2018) have been successfully used in this context.…”