Zero-Coupon Treasury Rates and Returns using the Volatility Index

2024/11/06 by Park, Jihyun, Sarantsev, Andrey
#60H10 #60J20 #60J60 #62J05 #62M10 #91B70 #91G30 #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Statistical Finance (q-fin.ST)

paper · doi:10.48550/arxiv.2411.03699

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.

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