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The formula is given in your link. For the real world probability without jump: $$x_t = x_{t-1} e^{-\eta \Delta t} + \hat{x}(1-e^{-\eta \Delta t}) +\sigma \sqrt{\frac{1-e^{- 2 \eta \Delta t}}{2 \eta}} N(0,1) $$ where: $x_t$: price $x_{t-1}$: PreviousPrice $\hat{x}$: long term mean (a parameter) $\Delta t$: Time step (one fraction) $\eta$: ...


3

1) The reversion speed $\eta$ is just a scaling factor >0 to control the sensitivity to mean deviations, it has no unit as such. 2) There are various simulation formulas in your reference link. Can you please specify which of these you want to simulate?



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