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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.

MSC:

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)
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