Pricing Bermudan Swaption under Two Factor Hull-White Model with Fast Gauss Transform

Paper: arXiv 2212.08250

Authors: Tomohisa Yamakami, Yuki Takeuchi

Abstract

This paper describes a fast and stable algorithm for evaluating Bermudan swaption under the two factor Hull-White model. We discretize the calculation of the expected value in the evaluation of Bermudan swaption by numerical integration, and Gaussian kernel sums appears in it. The fast Gauss transform can be applied to these Gaussian kernel sums, and it reduces computational complexity from $O(N^2)$ to $O(N)$ as grid points number $N$ of numerical integration. We also propose to stabilize the computation under the condition that the correlation is close to $-1$ by introducing the grid rotation. Numerical experiments using actual market data show that our method reduces the computation time significantly compared to the method without the fast Gauss transform. They also show that the method of the grid rotation contributes to computational stability in the situations where the correlation is close to $-1$ and time step is short.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sound application of the Fast Gauss Transform to the multi-factor Hull-White model, efficiently reducing computational complexity to O(N). Empirical rigor is solid, leveraging real market data to demonstrate efficiency gains and numerical stability via grid rotation under extreme correlation conditions.

Research Flowchart

  flowchart TD
    A[Goal: Fast & Stable Bermudan Swaption Pricing under 2-Factor Hull-White Model] --> B[Inputs: Market Data, Model Parameters & Interest Rate Curves]
    B --> C[Method: Discretize Expected Value via Numerical Integration]
    C --> D[Apply Fast Gauss Transform to Gaussian Kernel Sums]
    C --> E[Apply Grid Rotation Technique]
    D --> F[Process: Reduce Complexity from O N^2 to O N]
    E --> G[Process: Stabilize Computation when Correlation approx -1 & Time Step is Short]
    F & G --> H[Outcomes: Significant Reduction in Computation Time & Enhanced Numerical Stability]