Implementation of a Commitment Machine for an Adaptive and Robust Expected Shortfall Estimation.

Marco Bagnato,Pier Giuseppe Giribone,Anna Bottasso

doi:10.3389/frai.2021.732805

Marco Bagnato, Pier Giuseppe Giribone + Show 1 more

Open Access

https://doi.org/10.3389/frai.2021.732805

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Abstract

This study proposes a metaheuristic for the selection of models among different Expected Shortfall (ES) estimation methods. The proposed approach, denominated “Commitment Machine” (CM), has a strong focus on assets cross-correlation and allows to measure adaptively the ES, dynamically evaluating which is the most performing method through the minimization of a loss function. The CM algorithm compares four different ES estimation techniques which all take into account the interaction effects among assets: a Bayesian Vector autoregressive model, Stochastic Differential Equation (SDE) numerical schemes with Exponential Weighted Moving Average (EWMA), a Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) volatility model and a hybrid method that integrates Dynamic Recurrent Neural Networks together with a Monte Carlo approach. The integration of traditional Monte Carlo approaches with Machine Learning technologies and the heterogeneity of dynamically selected methodologies lead to an improved estimation of the ES. The study describes the techniques adopted by the CM and the logic behind model selection; moreover, it provides a market application case of the proposed metaheuristic, by simulating an equally weighted multi-asset portfolio.

Highlights

The cross correlation of assets and the time-varying behavior of conditional volatility are two important risk factors for an investment portfolio
The analysis is divided into two steps: a disaggregated analysis of the performances of each Commitment Machine (CM) on the days in which one of the four methods has been selected (NAR Monte Carlo Expected Shortfall (ES), standard Monte Carlo with Exponential Weighted Moving Average (EWMA) ES, standard Monte Carlo Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) ES, Bayesian ES) and a general analysis of the performances of the CM over the entire dataset
The cumulative loss on a certain date t is equal to the sum of the historical values from 0 to t of the loss function specified in The Commitment Machine in Eq 13 and it represents the total amount of losses below the ES threshold up to that day

Summary

Introduction

The cross correlation of assets and the time-varying behavior of conditional volatility are two important risk factors for an investment portfolio. Volatility tends to grow during periods of financial crisis, as shown for example by Ang and Chen (2002). This leads to periods of volatility clustering where conditional, short term volatility is very different from the long term unconditional one, with substantial effects on portfolio shocks that can be modeled through GARCH and EWMA volatility models. The objective of this work is to create a Risk Management system able to estimate the coherent statistical measure of Expected Shortfall through the implementation of models that take into account the cross-correlation between assets and the trend of variance clustering over time; the study suggests a possible solution to the problem of selecting adaptively the most performing ES models.

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