Paper: arXiv 2605.00862

Authors: Christian P. Fries

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical derivation of liquidity forecasting frameworks using change-of-numeraire and adjoint differentiation, but lacks an empirical section or a backtest of the proposed LVA adjustment on market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Reconcile Cash-Flow Forecasting with Replication] --> B[Inputs: Derivative Payoffs & Stochastic Settlement Lags]
    B --> C[Methodology: Compare Expected Cash-flows vs. Funding Sensitivities]
    C --> D[Computational Process: American Monte Carlo with Adjoint Differentiation]
    D --> E[Key Finding: Sensitivities align Forecasting with Self-Financing Replication]
    E --> F[Outcome: Proposal of Liquidity Valuation Adjustment - LVA]

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