Oil Option Value via Discounting

This quant interview question is about valuing a simple equity option written on a company whose payoff depends on a discrete uncertainty, here modeled with two possible outcomes. It sits at the intersection of option pricing, probability, and basic corporate valuation, and fits naturally into any quant prep sequence focused on contingent claims. Even though it looks like a story about commodities, the mathematical structure is exactly that of a vanilla call on a risky asset.

It trains comfort with expected values, risk-neutral thinking, and recognizing when an option is in the money or worthless. It forces candidates to translate a narrative about business success or failure into precise payoffs and probabilities, then aggregate them into a fair value. It also reinforces the difference between underlying value and derivative value.

This matters for quant interviews because it tests whether candidates can quickly interpret a financial scenario, abstract it into a payoff diagram, and apply core option pricing logic without formulas or models. Interviewers use such problems to assess probabilistic intuition, derivative pricing fundamentals, and readiness for more advanced quant prep topics like binomial trees and Monte Carlo methods, all essential in trading, risk, and research roles.

What it tests

The core structure here is the valuation of contingent claims: instruments whose payoff depends on the outcome of an underlying event. The fair value of such a claim is the expected payoff, calculated by weighting each possible outcome's payoff by its probability. This approach holds because, under risk-neutral valuation (or in the absence of discounting and arbitrage), the price of a derivative must reflect the average outcome, not the most likely one. The key is that the option only has value in scenarios where it is 'in the money'—that is, where exercising it yields a positive payoff. This logic generalizes to any situation where a contract's value is conditional on underlying events: enumerate the outcomes, compute the payoff in each, and take the probability-weighted sum.