On Deep Learning for computing the Dynamic Initial Margin and Margin Value Adjustment

ArXiv ID: 2407.16435 “View on arXiv”

Authors: Unknown

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.

Keywords: Dynamic Initial Margin (DIM), Counterparty credit risk, Neural networks, Monte Carlo simulation, Hull-White model, Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: 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.

  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"]