Hull-White Model

A Sinusoidal Hull-White Model for Interest Rate Dynamics: Capturing Long-Term Periodicity in U.S. Treasury Yields ArXiv ID: 2506.06317 “View on arXiv” Authors: Amit Kumar Jha Abstract This study is motivated by empirical observations of periodic fluctuations in interest rates, notably long-term economic cycles spanning decades, which the conventional Hull-White short-rate model fails to adequately capture. To address this limitation, we propose an extension that incorporates a sinusoidal, time-varying mean reversion speed, allowing the model to reflect cyclic interest rate dynamics more effectively. The model is calibrated using a comprehensive dataset of daily U.S. Treasury yield curves obtained from the Federal Reserve Economic Data (FRED) database, covering the period from January 1990 to December 2022. The dataset includes tenors of 1, 2, 3, 5, 7, 10, 20, and 30 years, with the most recent yields ranging from 1.22% (1-year) to 2.36% (30-year). Calibration is performed using the Nelder-Mead optimization algorithm, and Monte Carlo simulations with 200 paths and a time step of 0.05 years. The resulting 30-year zero-coupon bond price under the proposed model is 0.43, compared to 0.47 under the standard Hull-White model. This corresponds to root mean squared errors of 0.12% and 0.14%, respectively, indicating a noticeable improvement in fit, particularly for longer maturities. These results highlight the model’s enhanced capability to capture long-term yield dynamics and suggest significant implications for bond pricing, interest rate risk management, and the valuation of interest rate derivatives. The findings also open avenues for further research into stochastic periodicity and alternative interest rate modeling frameworks. ...

On Deep Learning for computing the Dynamic Initial Margin and Margin Value Adjustment ArXiv ID: 2407.16435 “View on arXiv” Authors: Unknown Abstract The present work addresses the challenge of training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk, a task traditionally burdened by the high costs associated with generating training datasets through nested Monte Carlo (MC) simulations. By condensing the initial market state variables into an input vector, determined through an interest rate model and a parsimonious parameterization of the current interest rate term structure, we construct a training dataset where labels are noisy but unbiased DIM samples derived from single MC paths. A multi-output neural network structure is employed to handle DIM as a time-dependent function, facilitating training across a mesh of monitoring times. The methodology offers significant advantages: it reduces the dataset generation cost to a single MC execution and parameterizes the neural network by initial market state variables, obviating the need for repeated training. Experimental results demonstrate the approach’s convergence properties and robustness across different interest rate models (Vasicek and Hull-White) and portfolio complexities, validating its general applicability and efficiency in more realistic scenarios. ...