Paper: arXiv 2312.14044

Abstract

This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models which cannot be completely realistic, and a discontinuity at default time. We leverage recent advances on risk-averse Reinforcement Learning developed specifically for option hedging with an ad hoc practice-aligned objective function aware of pathwise volatility, generalizing them to stochastic horizons. We formalize accurately the evolution of the hedger’s portfolio stressing such aspects. We showcase the efficacy of our approach by a numerical study for a portfolio composed of a single FX forward contract.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces advanced mathematical concepts like stochastic horizons and risk-averse RL with detailed formalization, indicating high math complexity; the empirical section includes a numerical study on an FX forward with transaction costs and collateral, showing implementation-heavy backtesting, but without public code/datasets, leading to a mid-high rigor score.

Research Flowchart

  flowchart TD
  A["Research Goal: CVA Hedging<br>for FX Forwards"] --> B["<b>Problem:</b><br>Sensitivities-based hedging<br>sub-optimal due to costs<br>& realistic constraints"]
  B --> C["<b>Methodology:</b><br>Risk-Averse Reinforcement Learning<br>Stochastic Horizon Policy<br>Pathwise Volatility Objective"]
  C --> D["<b>Inputs:</b><br>FX Forward Portfolio<br>Market Data (Spot, Vol, Rates)<br>Bid-Ask Spreads"]
  D --> E["<b>Process:</b><br>RL Agent optimizes<br>hedging strategy over<br>stochastic time paths"]
  E --> F["<b>Key Findings:</b><br>RL outperforms delta<br>hedging; effectively<br>manages CVA & costs"]