Mean-Reverting Random Walks

annual trend rate

annual standard deviation

mean start

months

months to trend

24

sample ending values

th 90 percentile end value	102.979
th 70 percentile end value	94.5259
th 50 percentile end value	88.0195
th 30 percentile end value	82.6403
th 10 percentile end value	73.2783

geometric mean of end values	87.926
arithmetic mean of end values	88.5932
standard deviation of end values	10.9619

Many financial or economic processes can be modeled as mean-reverting random walks. Mean-reverting walks differ from simple diffusion by the addition of a central expectation, usually growing with time, and a restoring force that pulls subsequent values toward that expectation. The random term is lognormally distributed, and the initial value of the mean can be above or below the series start. The strength of the restoring force is given in terms of the time to return to the mean. The plot shows sample paths which result in the

th

90

,

th

70

,

th

50

,

th

30

, and

th

10

percentiles in endpoint value, out of a larger sample.