Paper: arXiv 2401.13314

Abstract

Motivated by the equations of cross valuation adjustments (XVAs) in the realistic case where capital is deemed fungible as a source of funding for variation margin, we introduce a simulation/regression scheme for a class of anticipated BSDEs, where the coefficient entails a conditional expected shortfall of the martingale part of the solution. The scheme is explicit in time and uses neural network least-squares and quantile regressions for the embedded conditional expectations and expected shortfall computations. An a posteriori Monte Carlo validation procedure allows assessing the regression error of the scheme at each time step. The superiority of this scheme with respect to Picard iterations is illustrated in a high-dimensional and hybrid market/default risks XVA use-case.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an explicit scheme for complex anticipated BSDEs with heavy mathematical derivations and advanced concepts, demonstrating high mathematical complexity. It provides a simulation/regression scheme with a posteriori Monte Carlo validation and an empirical benchmark in a 36-dimensional XVA use-case, indicating substantial empirical rigor.

Research Flowchart

  flowchart TD
  Goal["Research Goal<br>Pathwise XVA via Fungible Capital"]
  Input["Data Inputs<br>Market Models & Counterparty Data"]
  
  Method["Methodology<br>Explicit Scheme via Neural Networks"]
  Process["Computational Process<br>Monte Carlo + Regression Steps"]
  
  Residual["A Posteriori Validation<br>Regression Error Assessment"]
  Outcome["Findings<br>Superiority over Picard Iterations"]
  
  Goal --> Input
  Input --> Method
  Method --> Process
  Process --> Residual
  Process --> Outcome