Cross-Sectional Learning of Extremal Dependence Among Financial Assets

Abstract

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random vectors featuring not only distinct marginal tail heaviness, but also flexible tail dependence structure. The novelty lies in that pairwise tail dependence between any two dimensions is modeled separately from their correlation, and can vary respectively according to its own parameter rather than the correlation parameter, which is an essential advantage over many commonly used methods such as multivariate t or elliptical distribution. It is also intuitive to interpret, easy to track, and simple to sample comparing to the copula approach. We show its flexible tail dependence structure through simulation. Coupled with a GARCH model to eliminate serial dependence of each individual asset return series, we use this novel method to model and forecast multivariate conditional distribution of stock returns, and obtain notable performance improvements in multi-dimensional coverage tests.Besides, our empirical finding about the asymmetry of tails of the idiosyncratic component as well as the whole market is interesting and worth to be well studied in the future.

Memory-Gated Recurrent Networks

“…The final performance is evaluated in the last 15, 000 observations. As mentioned earlier, all experiments are repeated with 10 pairs of randomly selected stocks reported in Yan, Wu, and Zhang (2019).…”

“…The coefficients of the AR processes (2) are arbitrarily fixed except for the constant terms, which are chosen to generate realistic time series. Table 2 of Yan, Wu, and Zhang (2019) reports the parameters of a few stocks. y 1 and y 2 are matched with a pair of stocks in the table.…”

“…To demonstrate the superiority of mGRN, we extensively test the model with simulated and real-world data sets. In the simulation study, the multivariate time series data are generated from the heavy-tailed model proposed in Yan, Wu, and Zhang (2019). We design a task such that a good pre-diction precisely requires the learning of both idiosyncratic and joint serial dependence.…”

“…In Yan, Wu, and Zhang (2019), function g(ω; u, v) is defined with u, v ≥ 1. The requirement is imposed to make sure the distribution is heavy tail, which is commonly observed in financial data.…”

Risk and return prediction for pricing portfolios of non-performing consumer credit

“…This is primarily because AI currently lacks (popular) methodologies for: i) effective probabilistic forecasting (as opposed to point forecasting in supervised machine learning), which is of great need in finance; ii) the dependence modeling of extremely high-dimensional variables. For the second one, [41] recently proposed a generative machine learning model for capturing tail dependence structure among stock returns. However, it remains a quite challenging task and needs more further research works.…”