Mean Reversion vs GBM Pricing

This question asks the candidate to compare option prices when the underlying is modeled by a mean-reverting process versus by a standard geometric Brownian motion. The setup is entirely conceptual: you are not computing a closed-form price, but reasoning about how the assumed dynamics of the underlying feed into the distribution of future prices and therefore into option value. This type of question is common in derivative pricing and risk roles, especially where models for commodities, interest rates, or volatility are used, since these markets often exhibit clear mean reversion rather than pure random walks.

To answer well, candidates must understand the link between the stochastic process, its variance over time, and how this maps into implied volatility in option pricing frameworks. It leans on intuition about transition distributions, long-run versus short-run volatility, and how constraints on price paths change tail probabilities. Interviewers are watching for clear reasoning about effective volatility, term structure of variance, and qualitative effects on in- and out-of-the-money options, without relying on memorized formulas. They also look for awareness of model risk when using GBM where mean reversion is more realistic.

What it tests

The core structure governing this class of problems is how the stochastic process underlying an asset's price determines the effective volatility that options experience. In standard models like geometric Brownian motion, volatility is constant and price changes are independent, so the option's value depends only on this fixed volatility. When the process is mean-reverting, such as in an Ornstein-Uhlenbeck process, the asset is statistically pulled back toward a long-term mean, which dampens large deviations and reduces the probability of extreme outcomes. This mean-reverting force lowers the effective volatility over time, typically reducing the option's value compared to a non-reverting process. The key is that option pricing is fundamentally about the distribution of possible future prices, and mean reversion compresses this distribution relative to a random walk.