Abstract
In this article, we study a bond market where short rates evolve as
where \(g : (0,\infty ) \rightarrow \mathcal{R}\) is deterministic, σ ≥ 0 is also deterministic, and W is the stochastic Wiener measure. Processes of this type are also called Brownian semistationary processes and they are particular cases of ambit processes. These processes are, in general, not of the semimartingale kind. We also study a fractional version of the Cox–Ingersoll–Ross model. Some calibration and simulations are also done.
Received 12/1/2011; Accepted2/23/2012; Final 4/3/2012
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Acknowledgements
The work of José Manuel Corcuera and Gergely Farkas is supported by the MCI Grant No. MTM2009-08218.
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Corcuera, J.M., Farkas, G., Schoutens, W., Valkeila, E. (2013). A Short Rate Model Using Ambit Processes. In: Viens, F., Feng, J., Hu, Y., Nualart , E. (eds) Malliavin Calculus and Stochastic Analysis. Springer Proceedings in Mathematics & Statistics, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5906-4_24
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DOI: https://doi.org/10.1007/978-1-4614-5906-4_24
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