Dynamic debt issuance with jumps

• Published in: Mathematics and financial economics Vol. 17; no. 4; pp. 663 - 694
• Main Authors: Minca, Andreea, Wissel, Johannes
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Assets; Bankruptcy; Banks; Barriers; Debt; Debt financing; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Endogenous; Equity; Finance; Insurance; Macroeconomics/Monetary Economics//Financial Economics; Management; Mathematics; Mathematics and Statistics; Quantitative Finance; Statistics for Business
• ISSN: 1862-9679; 1862-9660
• DOI: 10.1007/s11579-023-00347-7

We analyze debt issuance when the issuer’s asset is subject to downward jump risk. In equilibrium, we determine the debt capacity and identify an illiquidity barrier (or bank run trigger). When the asset-to-debt ratio is above the barrier, the issuer remains liquid; however, when it falls below the barrier, the issuer can no longer raise sufficient debt and faces liquidation. We demonstrate that a large negative shock will lead to a bank run in the next period, and the marginal lender rationally accounts for this. In contrast, the effect of a small shock is regime-dependent, leading to bank runs only outside an endogenous investment-grade region. The final equity exhibits a strong non-linear dependence on the minimal asset-to-debt ratio required by a regulator: beyond a certain level, there is a significant increase of the expectation accompanied by a sharp decrease in the variance of the equity at the time horizon (end equity). However, intermediate values for the asset-to-debt minimal ratios can lead to a shrinking investment-grade region and a substantial increase in the variance of end equity.