\begin{abstract}
This paper develops a structural--copula framework for modelling banks’ counterparty credit risk under funding and liquidity stress, focusing on the interaction between derivative valuation, balance-sheet constraints, and default dependence. The framework is motivated by the limitations of standard counterparty credit risk measures, such as CVA-based Value-at-Risk and Expected Shortfall, which primarily capture mark-to-market volatility and rely on reduced-form default specifications that abstract from liquidity-driven balance-sheet dynamics. Recent financial crises have highlighted the central role of funding constraints in amplifying counterparty risk and systemic contagion, motivating the need for models that explicitly link liquidity stress to default and exposure. The core object of analysis is the collateral- and funding-inclusive bilateral valuation adjusted (CFBVA) price of a derivative contract. This valuation functional incorporates credit valuation adjustment (CVA), debit valuation adjustment (DVA), collateral margining costs, and funding and investing costs within a unified risk-neutral pricing framework. The resulting pricing equation defines an asymmetric random variable whose distribution reflects both counterparty default risk and funding liquidity effects. Exposure is evaluated at a random time corresponding to the first default event between counterparties. A central feature of the proposed model is the endogenous generation of default through a balance-sheet liquidity constraint. Default is defined as the event in which the Net Stable Funding Ratio (NSFR) falls below its regulatory threshold, producing a structural stopping time rather than an exogenously specified default intensity. In contrast to reduced-form (intensity-based) models, where default arrival is imposed independently of valuation and funding dynamics, default in this framework arises endogenously from liquidity stress and directly interacts with exposure valuation. This structural specification allows liquidity conditions to influence both the timing of default and the magnitude of losses at default. To capture dependence between counterparty exposure and funding-side asset values at the default time, we employ bivariate Archimedean copulas. This approach allows for flexible modelling of non-linear dependence and tail dependence, which are central to credit contagion and wrong-way risk. Within this setting, we define a conditional credit Value-at-Risk (CoVaR) measure as the conditional quantile of the exposure distribution given a liquidity-stress event. Using copula-based representations of conditional distributions, we derive closed-form expressions for the conditional quantiles in terms of the copula generator and the marginal distributions of exposure and funding assets. The resulting liquidity-adjusted CoVaR extends existing systemic risk and CoVaR methodologies by conditioning on balance-sheet-driven liquidity stress rather than market return shocks. From a mathematical finance perspective, the framework contributes a tractable conditional risk measure defined on a valuation functional with endogenous stopping times and asymmetric payoffs. From an applied perspective, the model provides a coherent link between derivative pricing adjustments, funding liquidity, and counterparty default dependence. The framework also admits portfolio-level aggregation, enabling the analysis of credit contagion, tail dependence, and loss amplification across interconnected counterparties, making it suitable for applications in counterparty credit risk management and stress testing.
\end{abstract}

This is joint work with Sudheesh Kumar Kattumannil.