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Analysis of bank leverage via dynamical systems and deep neural networks

Lillo, Fabrizio, Livieri, Giulia, Marmi, Stefano, Solomko, Anton and Vaienti, Sandro (2023) Analysis of bank leverage via dynamical systems and deep neural networks. SIAM Journal on Financial Mathematics, 14 (2). pp. 598-643. ISSN 1945-497X

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Identification Number: 10.1137/21M1412517

Abstract

We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using value-at-risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system of slow-fast type associated with a unimodal map on [0,1] with an additive heteroscedastic noise whose variance is related to the portfolio rebalancing frequency to target leverage. In absence of noise the model is purely deterministic and the parameter space splits into two regions: (i) a region with a globally attracting fixed point or a 2-cycle; (ii) a dynamical core region, where the map could exhibit chaotic behavior. Whenever the model is randomly perturbed, we prove the existence of a unique stationary density with bounded variation, the stochastic stability of the process, and the almost certain existence and continuity of the Lyapunov exponent for the stationary measure. We then use deep neural networks to estimate map parameters from a short time series. Using this method, we estimate the model in a large dataset of US commercial banks over the period 2001-2014. We find that the parameters of a substantial fraction of banks lie in the dynamical core, and their leverage time series are consistent with a chaotic behavior. We also present evidence that the time series of the leverage of large banks tend to exhibit chaoticity more frequently than those of small banks.

Item Type: Article
Additional Information: © 2023 Society for Industrial and Applied Mathematics Publications.
Divisions: Statistics
Subjects: H Social Sciences > HG Finance
H Social Sciences > HA Statistics
Q Science > QA Mathematics
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C60 - General
G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure
Date Deposited: 04 Aug 2023 11:00
Last Modified: 19 May 2024 01:15
URI: http://eprints.lse.ac.uk/id/eprint/119917

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