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

TL;DR

This paper proposes a method for cash-flow forecasting in derivatives that aligns with replication strategies by using discounting sensitivities, and introduces a liquidity valuation adjustment for settlement lags.

Contribution

It clarifies the relation between cash-flow forecasting, risk-neutral valuation, and replication, proposing the use of sensitivities over expected cash-flows for consistency.

Findings

Using discounting sensitivities aligns forecasting with replication strategies.

A liquidity valuation adjustment captures settlement lags and timing frictions.

Implementation can be done via American Monte Carlo with adjoint differentiation.

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.