The average reversion rate was 0.42 and the average mutation rate was 0.33.
With this approach we estimated the mean kinetic dark reversion rate to be kr = 0.03 [min−1] (see Table 1).
Of course there is no theoretical basis for mean reversion to a real rate different from the one associated with PPP either.
where B t),t ≥ 0 is a standard Brownian motion, d r(t) is the change in the short-term interest rate, a is the speed of mean reversion, b is the average interest rate, and σ is the volatility of the short rate.
α is the intercept and κ, when positive, is the rate of mean reversion.
Third, evidence of mean reversion of the real exchange rate is regarded as evidence of purchasing power parity, but there is no guarantee that the mean to which a real exchange rate measure constructed using price indexes reverts is the PPP level.
The stochastic differential equation (SDE) for the Ornstein-Uhlenbeck process [5, 9] is given by dS_{t}=lambda(mu-S_{t} ),dt+sigma,dW_{t}, (1) where λ is the rate of mean reversion, μ is the long-run mean, σ is the volatility of the process, which all are strictly positive, and (W_{t}) denotes the Wiener process.
Vasicek [1] proposed the following classical Vasicek model which is defined by an equation of the form mathrm{d}r_{t}=alpha (beta -r_{t}),mathrm{d}t+sigma, mathrm{d}B_{t}, (1.1) where α is the rate of mean reversion, β is the long-run level, σ is the volatility coefficient, and (B_{t}) is a standard Brownian motion.
It was the first one to capture mean reversion, an essential characteristic of the interest rate that sets it apart from other financial prices.
The original SABR model was imperfect, in the sense that it lacked a few desirable features: the mean reversion of volatility, the interaction between different forward rates (which are assumed to be independent), and the possibility of calibrating the parameters to multiple maturities, for instance.
