Zero-Coupon Treasury Rates and Returns using the Volatility Index
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929682827444224 |
|---|---|
| author | Park, Jihyun Sarantsev, Andrey |
| author_facet | Park, Jihyun Sarantsev, Andrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-Coupon Treasury Rates and Returns using the Volatility Index Park, Jihyun Sarantsev, Andrey Statistical Finance Probability Applications 60H10, 60J20, 60J60, 62J05, 62M10, 91B70, 91G30 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. |
| title | Zero-Coupon Treasury Rates and Returns using the Volatility Index |
| topic | Statistical Finance Probability Applications 60H10, 60J20, 60J60, 62J05, 62M10, 91B70, 91G30 |
| url | https://arxiv.org/abs/2411.03699 |