Modelling Bounded Stochastic Motion

8 Pages Posted: 13 Jul 2019

See all articles by Chi-Fai Lo

Chi-Fai Lo

The Chinese University of Hong Kong

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department

Date Written: July 12, 2019


In this paper a simple stochastic approach has been presented for modelling financial observables which are constrained to lie between two positive bounds. While the proposed stochastic process has an inaccessible upper boundary, the lower boundary is quasi-bounded, implying that the lower boundary can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the lower boundary can thus provide us an indicator of possible downside risk of the corresponding observables. Empirical calibration of model parameters of the proposed process for different financial observables can also be easily performed due to the availability of an analytically tractable probability density function. Hence, in terms of the calibrated model parameters, making predictions of future movements of these observables becomes feasible.

Keywords: Constrained stochastic motion, quasi-bounded process, time-varying boundaries, crash risk

Suggested Citation

Lo, Chi-Fai and Hui, Cho-Hoi, Modelling Bounded Stochastic Motion (July 12, 2019). Available at SSRN: or

Chi-Fai Lo (Contact Author)

The Chinese University of Hong Kong ( email )

Department of Physics
Shatin, N.T., Hong Kong

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department ( email )

Hong Kong

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