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A short rate model using ambit processes. (English) Zbl 1270.91100

Viens, Frederi (ed.) et al., Malliavin calculus and stochastic analysis. A Festschrift in honor of David Nualart. New York, NY: Springer (ISBN 978-1-4614-5905-7/hbk; 978-1-4614-5906-4/ebook). Springer Proceedings in Mathematics & Statistics 34, 525-553 (2013).
Summary: In this article, we study a bond market where short rates evolve as \[ r_t=\int _{-\infty}^{t}g(t-s)\sigma _{s}W(\mathrm{d}s) \] where \(g:(0,\infty )\rightarrow \mathbb R\) is deterministic, \(\sigma\geq 0\) 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 (CIR) model. Some calibration and simulations are also done.
For the entire collection see [Zbl 1261.60005].

MSC:

91G30 Interest rates, asset pricing, etc. (stochastic models)
91B25 Asset pricing models (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
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