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What this intraday price extremum question tests

This is a medium-difficulty probability question that combines continuous-time stochastic processes with the properties of Brownian motion. It is commonly asked at quantitative trading firms to assess whether a candidate understands the distribution of path extrema — not just ending values, but the highest point reached during a path.

The key insight is that under driftless Brownian motion, the probability that a price touches a given level is fundamentally different from the probability that it ends above that level. Solving this requires familiarity with the reflection principle or the known distribution of running maxima, rather than simple normal-distribution calculations. Candidates must recognize which properties of Brownian motion apply and set up the problem correctly before computing.

• Running maximum and path extrema of Brownian motion
• Reflection principle and its applications
• Relationship between volatility, time horizon, and extreme movement probability