Robust Yield Curve Estimation for Mortgage Bonds Using Neural Networks

TL;DR

Addressing robust yield-curve estimation in sparse mortgage-bond markets, the paper proposes a per-day neural-network approach with a loss that enforces smoothness and market-consistency by comparing to a risk-free benchmark. The method is evaluated on Swedish mortgage bonds against NSS and KR, showing enhanced robustness and stability, especially to outliers and data sparsity. The framework can accommodate domain constraints like alignment with SEKOIS, enabling practitioners to trade off accuracy against smoothness as needed. The work offers a practical tool for pricing, risk management, and trading in illiquid fixed-income markets.

Abstract

Robust yield curve estimation is crucial in fixed-income markets for accurate instrument pricing, effective risk management, and informed trading strategies. Traditional approaches, including the bootstrapping method and parametric Nelson-Siegel models, often struggle with overfitting or instability issues, especially when underlying bonds are sparse, bond prices are volatile, or contain hard-to-remove noise. In this paper, we propose a neural networkbased framework for robust yield curve estimation tailored to small mortgage bond markets. Our model estimates the yield curve independently for each day and introduces a new loss function to enforce smoothness and stability, addressing challenges associated with limited and noisy data. Empirical results on Swedish mortgage bonds demonstrate that our approach delivers more robust and stable yield curve estimates compared to existing methods such as Nelson-Siegel-Svensson (NSS) and Kernel-Ridge (KR). Furthermore, the framework allows for the integration of domain-specific constraints, such as alignment with risk-free benchmarks, enabling practitioners to balance the trade-off between smoothness and accuracy according to their needs.

Figures (6)

• Figure 1: Hyperparameter tuning for learning rate (LR), number of epochs, $\gamma_1$, and $\gamma_2$ in a falling market (3/6/2024). Left: varying LR and epochs. Center: varying $\gamma_2$. Right: varying $\gamma_1$.
• Figure 2: Robustness test for NSS, KR, and NN when perturbing the price of a bond with maturity 12.3Y by 3, 5, and 10% increase.
• Figure 3: Robustness test for NSS, KR, and NN when randomly dropping 1, 5, and 10 bonds from the dataset for 10 MC simulations. The solid line is the yield curve estimated using all bonds. The dashed lines show the curves after randomly dropping bonds.
• Figure 4: RMSE$_{\text{curve}}$ w.r.t to the previous day along with Hit Rate of RMSE < 10 bps over a period of 1 year.
• Figure 5: Stability test when estimating the yield of a specific maturity, namely, 6-month, 2-year, and 10-year, compare to the benchmark SEKOIS rate over a period of 1 year.