Martingale Intuition for Quant Interviews
Martingale intuition for quant interviews, focused on fair games, conditional expectation, random walks, stopping cautions, and overuse mistakes.
Advanced candidates encountering fair-game, stopping, and random-walk questions.
Fair-game intuition
A martingale is often introduced as a fair-game process: given what you know now, the expected future value is the current value.
Conditional expectation is the core
The key statement is conditional. You are not saying the path will stay flat; you are saying the expected next value, given current information, equals the current value.
Random-walk example
A simple symmetric random walk has no drift. From a current position, the expected next position is the same current position because up and down moves balance.
Stopping caution
Stopping rules can change what is being measured. Optional stopping ideas require conditions, so do not casually claim every stopped fair game has the same expectation.
Interview use
Martingale intuition can help with fair games, random walks, and conditional expectation. Use it to explain structure, not to hide calculation.
Common mistakes
Candidates sometimes use martingale language as a shortcut without checking the conditional expectation. First verify the fair-game property in the prompt.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.