Replication-Consistent Liquidity Forecasting for Derivatives -- Forward Funding Sensitivities and a Liquidity Valuation Adjustment for Settlement Lags

Abstract

We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve hedge ratios) instead of "expected cash-flows" aligns forecasting with the self-financing replication strategy and avoids measure-mixing/aggregation issues. We then illustrate how a standard valuation model delivers pathwise funding requirements and propose a simple liquidity valuation adjustment to capture settlement lags and related timing frictions. The note provides implementation hints (American Monte Carlo with adjoint differentiation) and clarifies when "expected cash-flows" are informative and when sensitivities should be used instead.