Paper: arXiv 2407.16435

Abstract

The present work addresses the challenge of training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk, a task traditionally burdened by the high costs associated with generating training datasets through nested Monte Carlo (MC) simulations. By condensing the initial market state variables into an input vector, determined through an interest rate model and a parsimonious parameterization of the current interest rate term structure, we construct a training dataset where labels are noisy but unbiased DIM samples derived from single MC paths. A multi-output neural network structure is employed to handle DIM as a time-dependent function, facilitating training across a mesh of monitoring times. The methodology offers significant advantages: it reduces the dataset generation cost to a single MC execution and parameterizes the neural network by initial market state variables, obviating the need for repeated training. Experimental results demonstrate the approach’s convergence properties and robustness across different interest rate models (Vasicek and Hull-White) and portfolio complexities, validating its general applicability and efficiency in more realistic scenarios.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts including stochastic calculus, neural network theory for function approximation, and Monte Carlo methods for DIM computation, requiring dense theoretical derivations. It demonstrates empirical validation through convergence properties and robustness tests across interest rate models and portfolio complexities, though it lacks explicit code or dataset links.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Efficient DIM Computation"] --> B["Methodology<br>ML-based Parametric Model"]
  B --> C["Input: Market State Vector"]
  C --> D["Computation<br>Single Path Monte Carlo"]
  D --> E["Training<br>Multi-Output Neural Network"]
  E --> F["Output<br>Time-Dependent DIM Function"]
  F --> G["Findings<br>Validated across Interest Rate Models"]

Cited References (48)

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and 40 more
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1 of 48 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.