Zero-Coupon Treasury Rates and Returns using the Volatility Index
Abstract
We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data from 1990. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S&P 500 stock market index. Surprisingly, this stock index volatility works for Treasury bonds, too. Next, we prove long-term stability and the Law of Large Numbers. We express total returns of zero-coupon bonds using these principal components. We prove the Law of Large Numbers for these returns. All results are done for discrete and continuous time.
Keywords
Cite
@article{arxiv.2411.03699,
title = {Zero-Coupon Treasury Rates and Returns using the Volatility Index},
author = {Jihyun Park and Andrey Sarantsev},
journal= {arXiv preprint arXiv:2411.03699},
year = {2025}
}
Comments
22 pages, 3 figures, 8 graphs. Keywords: total returns, Ornstein-Uhlenbeck process, ergodic Markov processes, autoregression, long-term stability, stationary distribution, principal component analysis