The article introduces a new method to accurately price both interest rates and interest rate derivatives by considering the impact of yield curve residuals. By analyzing data on interest rates and derivatives, the researchers developed a model with yield curve factors and residual factors. They found that even small residuals on the yield curve can significantly affect the pricing of interest rate derivatives. The study shows that yield curve residuals are a recurring phenomenon that can amplify the pricing of options, especially at the ends of the yield curve. Incorporating these residual factors improves the accuracy of pricing interest rate derivatives.