Estimating the Waiting Time for a Stock to Reach a Price

Summary

The question asks how long it takes a stock’s historical price to reach a chosen level. The answer explains that there is no model-free estimate: the waiting-time distribution depends on assumptions about how prices evolve.

Under an arithmetic Brownian motion model, the expected time to hit a specified price is infinite, although a probability density for the waiting time can be derived. The answer raises geometric Brownian motion as a possible alternative but provides no formula or analysis for it. These results concern idealized price processes, so they do not directly establish how long a real stock will take to reach a target.

Key ideas

• A price target’s waiting time depends on the assumed price-generating process.
• Under arithmetic Brownian motion, the expected time to reach a level is infinite.
• A waiting-time probability density can still be derived under that model.
• The document does not provide a corresponding result for geometric Brownian motion.

Tags

# How to calculate the elapsed time until a stock reach a certain price?


# How to calculate the elapsed time until a stock reach a certain price?












In specific, I will set a certain price to a stock and I want to know how long takes until the historical prices reach this price. Thanks you.

## Answer by onlyvix.blogspot.com (score 0)

https://quant.stackexchange.com/a/29512

Well, there's no simple answer, but with some assumptions on price generating process you can try to come up with some estimates. If you assume ABM, then your expected time until a price reaches a certain level is infinite [1]. But you can also derive probability density of how long you would have to wait [2].

Maybe some smarter forum member would add if there are similar formulas for GBM.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.