Straddle Payoff on a Standard Normal

This quant interview question is about the expected payoff of a symmetric options strategy when the underlying follows a standard normal distribution. It connects option payoffs to properties of the normal law and asks you to translate a trading payoff into a precise probabilistic quantity. Because it involves a payoff that depends on the magnitude rather than the sign of the move, it highlights symmetry and absolute values in a continuous setting, which is central in advanced quant prep.

It trains your fluency with expectations of nonlinear functions, especially absolute values of Gaussian variables, and your comfort with expressing results in closed form involving mathematical constants. It also reinforces your ability to manipulate distributions, recognize symmetry, and deal with squared expectations, which show up in variance and risk calculations in quant interviews.

This matters for quant interviews because it sits exactly at the intersection of derivatives intuition and probability theory. Being able to compute and simplify such expectations is a core skill for pricing, risk modeling, and PnL attribution. On platforms like MyQuantPartner, mastering this type of question is key quant prep for roles in trading, research, and quantitative development, where interviews routinely probe these ideas.

What it tests

Whenever you are asked for the expected value of a function of a symmetric, continuous random variable—especially one like the standard normal—exploiting symmetry is crucial. For even functions (like the absolute value), the expectation over the whole real line can be written as twice the integral over the positive half, since the density and the function are both symmetric about zero. This often reduces the complexity of the calculation and avoids unnecessary work. The normal distribution's moment-generating properties and its closed-form integrals for powers and absolute values make it especially tractable for such expectations. The key is recognizing that the structure of the function (even/odd) and the distribution (symmetric/asymmetric) interact to simplify the integral dramatically, often allowing you to relate the expectation to known constants like $\pi$ or $e$.