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

Paper: arXiv 2402.15936

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (22)

1. Explainable neural network for pricing and universal static hedging of contingent claims (2022)
2. Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions (2009)
3. Valuing American options by simulation: a simple least-squares approach (2001)
4. The pricing of options and corporate liabilities (1973)
5. Neural networks for pattern recognition (1995)
6. Adam: A method for stochastic optimization (2014) — link
7. Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods (2012)
8. Valuation of the early-exercise price for options using simulations and nonparametric regression (1996)

0 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.