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Stochastic Volatilities and Correlations of Bond Yields

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  • BING HAN

Abstract

I develop an interest rate model with separate factors driving innovations in bond yields and their covariances. It features a flexible and tractable affine structure for bond covariances. Maximum likelihood estimation of the model with panel data on swaptions and discount bonds implies pricing errors for swaptions that are almost always lower than half of the bid–ask spread. Furthermore, market prices of interest rate caps do not deviate significantly from their no‐arbitrage values implied by the swaptions under the model. These findings support the conjectures of Collin‐Dufresne and Goldstein (2003), Dai and Singleton (2003), and Jagnnathan, Kaplin, and Sun (2003).

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  • Bing Han, 2007. "Stochastic Volatilities and Correlations of Bond Yields," Journal of Finance, American Finance Association, vol. 62(3), pages 1491-1524, June.
    • Handle: RePEc:bla:jfinan:v:62:y:2007:i:3:p:1491-1524
    DOI: 10.1111/j.1540-6261.2007.01242.x
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    Cited by:

    1. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    2. Almeida, Caio & Vicente, José, 2009. "Are interest rate options important for the assessment of interest rate risk?," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1376-1387, August.
    3. McConnell, John J. & Saretto, Alessio, 2010. "Auction failures and the market for auction rate securities," Journal of Financial Economics, Elsevier, vol. 97(3), pages 451-469, September.
    4. Hideyuki Takamizawa, 2018. "A term structure model of interest rates with quadratic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1173-1198, July.
    5. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    6. Hitesh Doshi & Hyung Joo Kim & Sang Byung Seo, 2023. "Options on Interbank Rates and Implied Disaster Risk," Finance and Economics Discussion Series 2023-054, Board of Governors of the Federal Reserve System (U.S.).
    7. Bisht Deepak & Laha, A. K., 2017. "Pricing Option on Commodity Futures under String Shock," IIMA Working Papers WP 2017-07-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Almeida, Caio & Vicente, José, 2009. "Identifying volatility risk premia from fixed income Asian options," Journal of Banking & Finance, Elsevier, vol. 33(4), pages 652-661, April.
    9. Kwai S. Leung & Hon Y. Ng & Hoi Y. Wong, 2014. "Stochastic Skew in the Interest Rate Cap Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1146-1169, December.
    10. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. Almeida, Caio & Graveline, Jeremy J. & Joslin, Scott, 2011. "Do interest rate options contain information about excess returns?," Journal of Econometrics, Elsevier, vol. 164(1), pages 35-44, September.
    12. Caio Almeida & Jos� Vicente, 2012. "Term structure movements implicit in Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 119-134, February.
    13. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    14. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    15. Markopoulou, Chryssa & Skintzi, Vasiliki & Refenes, Apostolos, 2016. "On the predictability of model-free implied correlation," International Journal of Forecasting, Elsevier, vol. 32(2), pages 527-547.
    16. Takamizawa, Hideyuki & 高見澤, 秀幸, 2015. "Impact of No-arbitrage on Interest Rate Dynamics," Working Paper Series G-1-5, Hitotsubashi University Center for Financial Research.
    17. Zhanyu Chen & Kai Zhang & Hongbiao Zhao, 2022. "A Skellam market model for loan prime rate options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(3), pages 525-551, March.

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