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Zero-Coupon Treasury Yield Curve with VIX as Stochastic Volatility

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  • Jihyun Park
  • Andrey Sarantsev

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. Next, we prove long-term stability for this discrete-time model and its continuous-time version. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S\&P 500 stock market index. It is surprising that this volatility, created for the stock market, also works for Treasury bonds. Since total returns of zero-coupon bonds can be easily found from these principal components, we prove long-term stability for total returns in discrete time.

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  • Jihyun Park & Andrey Sarantsev, 2024. "Zero-Coupon Treasury Yield Curve with VIX as Stochastic Volatility," Papers 2411.03699, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2411.03699
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    References listed on IDEAS

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