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The Wishart short rate model

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  • Alessandro Gnoatto

Abstract

We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves.

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  • Alessandro Gnoatto, 2012. "The Wishart short rate model," Papers 1203.5513, arXiv.org, revised May 2014.
    • Handle: RePEc:arx:papers:1203.5513
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    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 253-289, May.
    3. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
    4. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153, January.
    5. José Da Fonseca & Martino Grasselli & Florian Ielpo, 2011. "Hedging (Co)Variance Risk With Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
    6. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
    7. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    8. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    9. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    10. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748, arXiv.org, revised Aug 2013.
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    Cited by:

    1. Chiarella, Carl & Da Fonseca, José & Grasselli, Martino, 2014. "Pricing range notes within Wishart affine models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 193-203.
    2. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    3. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    4. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    5. Abdelkoddousse Ahdida & Aur'elien Alfonsi & Ernesto Palidda, 2014. "Smile with the Gaussian term structure model," Papers 1412.7412, arXiv.org, revised Nov 2015.
    6. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org, revised Aug 2015.
    7. Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    8. Claudio Fontana, 2022. "Caplet pricing in affine models for alternative risk-free rates," Papers 2202.09116, arXiv.org, revised Jan 2023.
    9. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
    10. Song, Jian & Yao, Jianfeng & Yuan, Wangjun, 2022. "Recent advances on eigenvalues of matrix-valued stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.

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