First Passage Time Interview Guide
First passage time interview guide for threshold crossing, hitting times, random walk examples, options links, and boundary caveats.
Candidates solving threshold, barrier, and hitting-time questions.
First passage time is first boundary hit
First passage time is the first time a process reaches a specified level or set. It appears in random walks, barriers, default models, and threshold problems.
Define the boundary and start
The answer depends on starting point, target boundary, lower boundary if any, and whether time is discrete or continuous. These details should be stated before solving.
Concrete example
For a random walk starting at 3 with target 10, the first passage time to 10 is the first step when the walk reaches 10, if it reaches it.
Hitting may not be guaranteed
Some processes may never hit the boundary, or may hit with probability less than one. Expected hitting time can be infinite even when hitting is possible.
Common mistakes
Candidates often compute a crossing probability without defining the crossing time. A strong answer separates probability of hit from time to hit.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.