Collateral Liquidations under Order Book Dynamics: A Formal Model for Aave and Compound

When ratios fall: A dynamic approach to contingent convertibles

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 ratios, share prices, and CoCo bond prices, incorporating both continuous market movements and correlated jump risk. The model advances existing literature through three key innovations: (1) a hybrid mechanism for modeling regulatory discretion in trigger decisions, (2) a class of power conversion schemes that generalizes traditional approaches while maintaining analytical tractability, and (3) a method to overcome the temporal discrepancy between high-frequency market data and low-frequency regulatory reporting. We derive semi-closed form formulas for both write-down and equity-convertible CoCo bonds and validate our model through five case studies spanning from 2009 to 2023, including an in-depth analysis of the 2023 Credit Suisse collapse. The results demonstrate a significant improvement in pricing and hedging performance while highlighting the model's data-adaptive nature that enables short-term predictions.

International Arbitrage Premia

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 four decades of international equity, currency, and factor returns, NAC is strongly countercyclical, peaking during crises when linear models turn negative. The implied Sharpe ratio increase reaches 0.3, underscoring its economic relevance. While linear models perform well on average, they fail in distressed states, underpricing nonlinear payoffs. Incorporating NAC restores positivity and stabilizes pricing across regimes. (JEL G11, G12, G15)

Determining Insolvency Regions in Banks: A Stochastic Dynamic Approach Integrating Liquidity and Credit Risk

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 loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead to endogenous insolvency. By incorporating Basel III regulatory requirements (LCR and NSFR) into a stochastic optimal control framework, we solve for the exact insolvency boundary using the Hamilton-Jacobi-Bellman (HJB) equation. To bridge the gap between theoretical complexity and supervisory practice, we derive and validate a surrogate analytical approximation function that allows for real-time monitoring. Calibrated using granular balance-sheet data from the Iranian banking sector, our model reveals significant non-linear threshold effects: the joint occurrence of liquidity stress and credit portfolio defaults disproportionately accelerates the transition toward insolvency compared to their individual effects. The proposed surrogate function offers supervisors a computationally efficient tool for stress testing and early warning systems. Our findings provide novel insights into financial frictions in emerging markets and offer a rigorous framework for integrated risk management.

Volatility Amplification Mechanisms of Leveraged ETFs and Policy Implications in Korea

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 results demonstrate that mechanical, pro-cyclical rebalancing concentrated at the market-on-close (MOC) induces directional distortion, systematically driving asset prices away from their fundamental values depending on market conditions. In particular, this study provides evidence that as the assets under management (AUM) of these linked products expand, the liquidity breakdown threshold of the limit order book declines steeply. Consequently, even minor illiquidity frictionscan cause mechanical selling pressure to escalate directly into tail risk. Drawing on these findings, this study offers policy implications to enhance macroprudential stability and prevent the transmission of microstructural risks into systemic risks. Specifically, we propose the introduction of dynamic AUM caps, the normalization of creation fees to mitigate structural conflicts of interest among Authorized Participants (APs), and restrictions on listing ultra-high leveraged products.

SUERF Policy Brief

Open-End Fund Investment with Dynamic Fund Flows and Passive Benchmarking: A Continuous-Time Stackelberg Game

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 combining a scale-dependent value-added objective with endogenous subscription and redemption jumps. Fund flows are represented by marked compound Poisson processes, and the manager acts as leader while a representative investor chooses participation as a follower. Under bounded controls, bounded Lipschitz jump intensities, admissible jump-size distributions, and strict-concavity conditions, we establish positivity and moment bounds for the state process, provide sufficient conditions for the existence and uniqueness of a Markov feedback Stackelberg equilibrium, and state a jump-diffusion verification theorem. A transparent local feedback approximation and Monte Carlo robustness exercise illustrate how redemption pressure, subscription intensity, jump-size dispersion, benchmark volatility, and risk aversion affect active exposure and terminal fund wealth. The results show that stronger redemption pressure and benchmark-relative risk reduce active positions, whereas subscription incentives increase risk-taking only when expected value added compensates for flow-induced dilution. Within its stated assumptions, the model provides a tractable theoretical benchmark rather than an empirically validated structural model.