Gamma vs Time Skew

This question focuses on comparing the gamma of two otherwise identical vanilla options that differ only in time to expiration, one being relatively short-dated and the other long-dated. The candidate is asked to reason about how the curvature of the option's price with respect to the underlying changes as maturity varies, and how that interacts with moneyness. It is a typical conceptual Greeks question used in derivatives, options trading, and risk-focused quant interviews, probing whether the candidate can mentally visualize the option payoff smoothing out over time versus becoming more "digital-like" close to expiry.

To answer it well, the candidate needs a solid grasp of gamma as the second derivative of option value with respect to the underlying and how it concentrates around the strike as time decreases. It leans on intuition about the shape of pricing curves, the asymptotic behavior near expiry, and the dependence of gamma on both time and distance from the strike. Interviewers look for clear reasoning, correct conditional statements about at-the-money versus deep in- or out-of-the-money regimes, and an ability to reconcile intuitive pictures with the formal definition of gamma.

What it tests

The core structure in option gamma questions is the relationship between an option's time to expiration and the sharpness of its payoff profile. As expiration approaches, the option's value function becomes increasingly kinked at the strike price, meaning its slope (delta) changes more abruptly for small moves in the underlying. This is reflected mathematically as a spike in gamma for at-the-money options near expiry: the second derivative of the option price with respect to the underlying becomes very large at the strike, because the option's value must rapidly transition from zero to intrinsic value. This pattern holds because, with less time, there is less smoothing from potential future movements, so the price curve becomes more locally sensitive to the spot price. The general principle is that gamma is highest for at-the-money options as expiry nears, but for deep in- or out-of-the-money options, longer time to expiry can allow for more curvature due to the possibility of moving into or out of the money.