Capital Regulation under Price Impacts and Dynamic Financial Contagion

TL;DR

This paper develops a continuous-time model to analyze how price impacts and capital regulation influence financial contagion, providing analytical bounds and stress testing tools for systemic risk assessment.

Contribution

It introduces a novel continuous-time framework incorporating price-mediated contagion and risk-weight constraints, with analytical bounds and exact formulas for stress testing.

Findings

Analytical bounds on risk-weights as a function of market liquidity

Existence and uniqueness of the joint system of firm behavior and asset prices

Exact formulas for stress testing the financial system

Abstract

We construct a continuous time model for price-mediated contagion precipitated by a common exogenous stress to the banking book of all firms in the financial system. In this setting, firms are constrained so as to satisfy a risk-weight based capital ratio requirement. We use this model to find analytical bounds on the risk-weights for assets as a function of the market liquidity. Under these appropriate risk-weights, we find existence and uniqueness for the joint system of firm behavior and the asset prices. We further consider an analytical bound on the firm liquidations, which allows us to construct exact formulas for stress testing the financial system with deterministic or random stresses. Numerical case studies are provided to demonstrate various implications of this model and analytical bounds.