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A Vasicek-type short rate model with memory effect. (English) Zbl 1332.60101

Summary: We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Although the model is non-Markov, there exists an associated Markov process that allows one to apply usual numerical methods to the model. We derive analogues of an affine term structure and term structure equations for the model, and, using them, we present a numerical method to evaluate contingent claims.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91G80 Financial applications of other theories
91G30 Interest rates, asset pricing, etc. (stochastic models)
91G20 Derivative securities (option pricing, hedging, etc.)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
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References:

[1] DOI: 10.1081/SAP-200050096 · Zbl 1108.91035 · doi:10.1081/SAP-200050096
[2] DOI: 10.1081/SAP-200050099 · Zbl 1108.91036 · doi:10.1081/SAP-200050099
[3] Avram F., Markov Processes and Related Fields 19 pp 249– (2013)
[4] DOI: 10.3150/bj/1116340291 · Zbl 1066.60071 · doi:10.3150/bj/1116340291
[5] DOI: 10.1098/rsta.1994.0067 · Zbl 0822.90015 · doi:10.1098/rsta.1994.0067
[6] DOI: 10.1111/j.1467-9965.1996.tb00123.x · Zbl 0915.90014 · doi:10.1111/j.1467-9965.1996.tb00123.x
[7] DOI: 10.1007/978-3-540-68015-4 · Zbl 1184.91002 · doi:10.1007/978-3-540-68015-4
[8] DOI: 10.1111/j.1467-9469.2007.00592.x · Zbl 1198.62078 · doi:10.1111/j.1467-9469.2007.00592.x
[9] Hull J.C., Options, Futures and Other Derivatives (2008) · Zbl 1087.91025
[10] Inoue A., Journal of Applied Mathematics and Stochastic Analysis (2006)
[11] DOI: 10.2307/2328284 · doi:10.2307/2328284
[12] DOI: 10.1016/0304-405X(77)90016-2 · Zbl 1372.91113 · doi:10.1016/0304-405X(77)90016-2
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