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A Framework for Waterfall Pricing Using Simulation-Based Uncertainty Modeling

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  • Nicola Jean
  • Giacomo Le Pera
  • Lorenzo Giada
  • Claudio Nordio

Abstract

We present a novel framework for pricing waterfall structures by simulating the uncertainty of the cashflow generated by the underlying assets in terms of value, time, and confidence levels. Our approach incorporates various probability distributions calibrated on the market price of the tranches at inception. The framework is fully implemented in PyTorch, leveraging its computational efficiency and automatic differentiation capabilities through Adjoint Algorithmic Differentiation (AAD). This enables efficient gradient computation for risk sensitivity analysis and optimization. The proposed methodology provides a flexible and scalable solution for pricing complex structured finance instruments under uncertainty

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  • Nicola Jean & Giacomo Le Pera & Lorenzo Giada & Claudio Nordio, 2025. "A Framework for Waterfall Pricing Using Simulation-Based Uncertainty Modeling," Papers 2507.13324, arXiv.org.
    • Handle: RePEc:arx:papers:2507.13324
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    References listed on IDEAS

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    1. Attilio Meucci, 2005. "Risk and Asset Allocation," Springer Finance, Springer, number 978-3-540-27904-4, July.
    2. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    3. Damiano Brigo & Claudio Nordio, 2010. "Liquidity-adjusted Market Risk Measures with Stochastic Holding Period," Papers 1009.3760, arXiv.org, revised Oct 2010.
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