Deep Hedging Bermudan Swaptions

ArXiv ID: 2411.10079 “View on arXiv”

Authors: Unknown

Abstract

Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero transaction costs, perfect liquidity, and continuous-time hedging, which often differ from real market environments. This discrepancy can lead to residual profit and loss (P&L), resulting in two primary issues. First, residual P&L may prevent achieving the initial model price, especially with improper parameter settings, potentially causing a negative P&L trend and significant financial impacts. Second, controlling the distribution of residual P&L to mitigate downside risk is challenging, as hedged positions may become curve gamma-short, making them vulnerable to large interest rate movements. The deep hedging approach enables flexible selection of convex risk measures and hedge strategies, allowing for improved residual P&L management. This study also addresses challenges in applying the deep hedging approach to Bermudan swaptions, such as efficient arbitrage-free market scenario generation and managing early exercise conditions. Additionally, we introduce a unique “Option Spread Hedge” strategy, which allows for robust hedging and provides intuitive interpretability. Numerical analysis results demonstrate the effectiveness of our approach.

Keywords: Deep Hedging, Bermudan Swaptions, Convex Risk Measures, Interest Rate Derivatives, Arbitrage-Free Pricing, Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper demonstrates high mathematical complexity through advanced stochastic calculus, derivative pricing models, and deep learning optimization, but provides substantial empirical validation via detailed numerical experiments and a unique ‘Option Spread Hedge’ strategy.

  flowchart TD
    Start(["Research Goal"]) -->|Address limitations of traditional Bermudan swaption hedging in real markets| Methodology
    
    subgraph Methodology ["Key Methodology"]
        A["Deep Hedging Framework"] -->|Convex Risk Measures| B["Option Spread Hedge Strategy"]
    end
    
    Inputs -->|Arbitrage-Free Market Scenarios<br>Efficient Generation| Computational
    
    subgraph Computational ["Computational Processes"]
        C["Training Deep Hedging Model<br>Manage Early Exercise Conditions"]
    end
    
    Methodology --> Computational
    Computational --> Outcomes
    
    subgraph Outcomes ["Key Findings"]
        D["Improved Residual P&L Management<br>Robust Hedge Performance"] --> E["Effective Mitigation of Downside Risk<br>Interpretability & Liquidity"]
    end
    
    style Start fill:#e1f5e1,stroke:#333,stroke-width:2px
    style Outcomes fill:#fff2cc,stroke:#333,stroke-width:2px