Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk

ArXiv ID: 2402.15936 “View on arXiv”

Authors: Unknown

Abstract

This paper presents a Monte-Carlo-based artificial neural network framework for pricing Bermudan options, offering several notable advantages. These advantages encompass the efficient static hedging of the target Bermudan option and the effective generation of exposure profiles for risk management. We also introduce a novel optimisation algorithm designed to expedite the convergence of the neural network framework proposed by Lokeshwar et al. (2022) supported by a comprehensive error convergence analysis. We conduct an extensive comparative analysis of the Present Value (PV) distribution under Markovian and no-arbitrage assumptions. We compare the proposed neural network model in conjunction with the approach initially introduced by Longstaff and Schwartz (2001) and benchmark it against the COS model, the pricing model pioneered by Fang and Oosterlee (2009), across all Bermudan exercise time points. Additionally, we evaluate exposure profiles, including Expected Exposure and Potential Future Exposure, generated by our proposed model and the Longstaff-Schwartz model, comparing them against the COS model. We also derive exposure profiles at finer non-standard grid points or risk horizons using the proposed approach, juxtaposed with the Longstaff Schwartz method with linear interpolation and benchmark against the COS method. In addition, we explore the effectiveness of various interpolation schemes within the context of the Longstaff-Schwartz method for generating exposures at finer grid horizons.

Keywords: Bermudan Options, Monte Carlo Simulation, Neural Network Pricing, Risk Management, Exposure Profiles

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including neural network theory, Fourier expansions (COS method), and Monte Carlo simulations with complex error convergence analysis. It also demonstrates strong empirical rigor through extensive comparative analysis against established benchmarks (Longstaff-Schwartz, COS), with specific implementation details for exposure profiles and interpolation schemes.

  flowchart TD
    A["Research Goal"] --> B["Generate Option & Market Data"]
    B --> C["Implement & Compare Models"]
    C --> D["Compute Prices & Exposures"]
    D --> E{"Benchmark Analysis & Findings"}
    
    B --> B1["Markovian /<br>No-Arbitrage Assumptions"]
    
    C --> C1["Proposed Neural Network<br>with Optimization"]
    C --> C2["Longstaff-Schwartz<br>with Interpolation"]
    C --> C3["COS Model<br>Benchmark"]
    
    D --> D1["PV Distributions"]
    D --> D2["Exposure Profiles<br>EP & PFE"]
    D --> D3["Interpolation Schemes"]
    
    E --> F["Key Outcomes"]
    
    F --> F1["NN Acceleration &<br>Convergence Analysis"]
    F --> F2["Accurate Static Hedging"]
    F --> F3["Refined Exposure Profiles<br>at Finer Grid Points"]