Comparing Pricing of Asian vs. European Options

This question contrasts the pricing of an Asian option, whose payoff depends on an average of the underlying asset price over time, with a plain-vanilla European option, whose payoff depends only on the terminal price at maturity. The candidate is asked to reason qualitatively about how this change in payoff definition affects value, assuming all other contract terms are aligned. It is a typical conceptual question in options or derivatives interviews, especially for roles that expect comfort with path dependence and intuition for how contract features trade off against price.

The discussion leans on understanding how option values are expectations of convex payoffs under a risk-neutral measure, and how volatility and payoff dispersion feed into that expectation. Candidates are expected to recognize that averaging alters the distribution of the effective underlying driving the payoff, and to connect that to reduced variance and fewer extreme scenarios. An interviewer is watching for correct use of convexity arguments, clear articulation of the link between volatility and option value, and the ability to generalize the reasoning to other path-dependent structures without resorting to memorized formulas.

What it tests

Options are priced based on the expected value of their payoffs, which is heavily influenced by the volatility of the underlying asset. When an option's payoff depends on an average (as in Asian options), the averaging process smooths out fluctuations, reducing the variance of the payoff distribution compared to options that depend solely on the terminal price (like European options). Lower variance means a lower probability of extreme outcomes, which are the main contributors to high option prices. This reduction in effective volatility directly translates to a lower option premium, since option value increases with volatility due to the convexity of the payoff function. The key insight is that any mechanism that reduces the dispersion of possible payoffs—such as averaging—will generally reduce the value of the option, all else equal.