How to calibrate Gaussian two-factor model using swaption

Area of Science:

• Quantitative Finance
• Financial Modeling
• Interest Rate Derivatives

Background:

• The Gaussian two-factor model is widely used for interest rate derivatives pricing.
• Accurate estimation of volatility parameters, particularly mean reversion, is crucial for model performance.
• Existing methods often struggle with parameter stability and model limitations.

Purpose of the Study:

• To propose an efficient approximation for swaption normal volatility.
• To enable separate estimation of the mean reversion parameter within the Gaussian two-factor model.
• To enhance the stability and robustness of volatility parameter estimation.

Main Methods:

• Developed a novel two-step approach for approximating swaption normal volatility.
• Implemented a method to isolate and estimate the mean reversion parameter.
• Compared the proposed two-step method against a simultaneous one-step calibration approach.

Main Results:

• The proposed two-step method yields more stable parameter estimates compared to the one-step method.
• The one-step method demonstrated excessive sensitivity to market fluctuations.
• The new approach effectively resolves several persistent problems within the Gaussian two-factor model.

Conclusions:

• The proposed two-step approximation offers a more stable and reliable way to estimate volatility parameters in Gaussian two-factor models.
• This method enhances the practical applicability of the model by improving parameter estimation accuracy.
• The findings suggest a significant improvement in interest rate derivative modeling through enhanced parameter stability.