Random Walk and Drift

[Onda]

In quants, we speak about random walk with drift and that if we have a drift, b₀ is different than 0, but what exactly is the drift supposed to mean?

[S2000magician]

It means that b₀ ≠ 0.

Literally, that’s the definition of drift.

Tomorrow’s value is expected to be larger than today’s.

Or, tomorrow’s value is expected to be smaller than today’s.

[Onda]

thanks magician

[S2000magician]

You’re welcome.

[Sartorial]

Does b sub-0 represent “the drift” in the random walk equation with a drift?

From Kaplan:

[S2000magician]

Yes; with drift means b₀ ≠ 0 and without drift means b₀ = 0.