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Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models

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  • Matthew Lorig
  • Natchanon Suaysom

Abstract

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accuracy of our approximation.

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  • Matthew Lorig & Natchanon Suaysom, 2022. "Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models," Papers 2212.04425, arXiv.org.
    • Handle: RePEc:arx:papers:2212.04425
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Matthew Lorig & Natchanon Suaysom, 2022. "Options on bonds: implied volatilities from affine short-rate dynamics," Annals of Finance, Springer, vol. 18(2), pages 183-216, June.
    5. Tim Leung & Matthew Lorig & Andrea Pascucci, 2017. "Leveraged Etf Implied Volatilities From Etf Dynamics," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1035-1068, October.
    6. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    7. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.
    8. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    9. Flavio Angelini & Stefano Herzel, 2006. "Notes and Comments: An approximation of caplet implied volatilities in Gaussian models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 113-127, February.
    10. Li Chen & Damir Filipović & H. Vincent Poor, 2004. "Quadratic Term Structure Models For Risk‐Free And Defaultable Rates," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 515-536, October.
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