Asymmetric short-rate model without lower bound

We propose a new short-rate process which appropriately captures the salient features of the negative interest rate environment. The model combines the advantages of the Vasicek and Cox-Ingersoll-Ross (CIR) dynamics: it is flexible, tractable and displays positive skewness without imposing a strict lower bound. In addition, a novel calibration procedure is introduced which focuses on minimizing the Kullback-Leibler (KL) divergence between the model- and market-implied forward rate densities rather than focusing on the minimization of price or volatility discrepancies. A thorough empirical analysis based on cap market quotes shows that our model displays superior performance compared to the Vasicek and CIR models regardless of the calibration method. Our proposed calibration procedure based the KL divergence better captures the entire forward rate distribution compared to competing approaches while maintaining a good fit in terms of pricing and implied volatility errors.