Processes with volatility-induced stationarity: An application for interest rates. (English) Zbl 1130.60072

Summary: We propose a refinement of the existing definition of volatility-induced stationarity that allows us to distinguish between processes with drift and diffusion induced stationarity and processes with pure volatility-induced stationarity. We also propose a classification of stationary processes with volatility-induced stationarity according to the volatility that is needed to inject stationarity. Processes with volatility-induced stationarity are potentially applicable to interest rate time-series since, as has been acknowledged, mean-reversion effects occur mainly in periods of high volatility. As such, we provide evidence that the logarithm of the Fed funds rate can be modelled as a local martingale with volatility-induced stationarity.


60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91G30 Interest rates, asset pricing, etc. (stochastic models)
Full Text: DOI


[1] DOI: 10.1093/rfs/9.2.385
[2] DOI: 10.1111/0022-1082.00149
[3] DOI: 10.1111/1468-0262.00274 · Zbl 1104.62323
[4] Arnold L., Stochastic Differential Equations: Theory And Application (1974) · Zbl 0278.60039
[5] DOI: 10.1016/S0304-405X(02)00135-6
[6] DOI: 10.1111/1468-0262.00395 · Zbl 1136.62365
[7] Bibby B., Bernoulli 1 pp 17– (1995)
[8] Chan K., The Journal of Finance pp 1210– (1992)
[9] X. Chen, and M. Carrasco(1998 ), Nonlinearity and Temporal Dependence , Unpublished. · Zbl 1431.62600
[10] DOI: 10.1111/0022-1082.00208
[11] DOI: 10.1093/rfs/10.3.525
[12] Cox J., Econometrica 53 pp 385– (1985)
[13] Hansen L., Econometrica 63 pp 767– (1995)
[14] DOI: 10.1198/073500104000000433
[15] Ikeda N., Stochastic Differential Equations and Diffusion Processes (1981) · Zbl 0495.60005
[16] Karlin S., A Second Course in Stochastic Processes (1981) · Zbl 0469.60001
[17] DOI: 10.1111/1368-423X.t01-1-00075 · Zbl 1006.60049
[18] DOI: 10.1017/S0266466603195035
[19] Nicolau J., Journal of Statistical Computation and Simulation (2005)
[20] DOI: 10.1093/rfs/11.3.449
[21] M. Richter(2002 ), A Study of Stochastic Differential Equations with Volatility Induced Stationarity , Unpublished.
[22] Skorokhod A., Asymptotic Methods in the Theory of Stochastic Differential Equation (1989) · Zbl 0695.60055
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