Sample Question #138 (mathematics – stochastics)

(The interviewer shows you a line chart that looks like a stock price chart, but with the y-axis labeled "50, 55, 60, 65," i.e., the smallest value on the line is no less than 10. The x-axis is unlabeled.)

This chart shows a random walk in progress. Now, answer the following:

1. What does the x-axis represent?

2. What’s the probability that this random walk will hit 0? How about -2,000?

3. If I tell you that the terminus of the random walk line represents its state at time *t*_{1}, what’s the probability that the random walk will hit 0 by some later time *t*_{2} > *t*_{1}?

(Comment: random walk questions are quite popular with quant interviewers, so you should know at least some basics)

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ANSWER

1. Time

2. 100% in both cases (Bonus question: what if this is a random walk with drift?)

3. There’s a formula for this, but I can’t remember it – can anyone give it to us? Thanks.