We develop a rigorous framework for modeling collateral liquidations in decentralized lending protocols such as Aave and Compound. In contrast to earlier approaches based on constant-product market maker (CPM) assumptions, real-world liquidations are executed through order books with finite depth. This introduces price impact, modifies solvency conditions, and reduces safe loan-to-value ratios. We introduce the Aggregate Value Function, defined directly on the order book, and establish its monotonicity, concavity, and quasi-linearity, following the quasi-linear order book framework. Building on these properties, we derive solvency inequalities and explicit formulas for safe leverage. Our model extends CPM-based theory to discrete liquidity environments and provides foundations for risk management and parameter design in lending protocols.
We propose a novel valuation framework for contingent convertible (CoCo) bonds based on the issuing bank's Common Equity Tier 1 (CET1) ratio, which is widely acknowledged as an indicator of a bank's solvency. Our approach develops a bivariate jump-diffusion model that captures the dynamic relationship linking the CET1...
We introduce the nonlinear arbitrage correction (NAC), the residual that renders a linear benchmark model arbitrage-free while preserving the law of one price. The price of NAC captures the marginal Sharpe ratio increase consistent with no-arbitrage and upper-bounds the constrained Hansen–Jagannathan distance. Using...
Mirela Sandulescu, P. Schneider· The Review of financial stud...· 0 citations
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback...
This study analyzes the microstructural mechanisms through which the rapidly expanding single-stock leveraged ETFs in the Korean capital market impede the price discovery function and amplify endogenous volatility. Based on a dynamic simulation utilizing the actual market scales of large-cap semiconductor stocks, the r...
Sun-Joong Yoon· Korean Journal of Financial...· 0 citations
This paper develops a stylized continuous-time framework for open-end fund investment in which state-dependent fund flows, passive benchmarking, and strategic manager–investor interaction are modeled jointly. The contribution is not a new Stackelberg solution concept; rather, it is the economic mechanism created by com...
Yin Li, Ya-Zhi Song, Can Zhou et al.· Mathematics· 0 citations
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