Predicting Tomorrow's Call Option Price

This interview question focuses on the expected evolution of a call option's price over a single day, starting from a known current value. The candidate is asked to reason about how an option, as a leveraged claim on an underlying asset, should be expected to move in equilibrium, rather than to compute a specific numerical forecast. The setup sits at the intersection of options theory and asset pricing: the option is already priced today by the market, and the task is to infer what, in expectation, should happen to that price tomorrow under standard equilibrium assumptions.

Answering well relies on comfort with the Capital Asset Pricing Model, the notion of beta for derivative securities, and the relationship between risk, expected return, and leverage. Strong candidates recognize that an option's expected return reflects its systematic risk exposure, not just the drift of the underlying or risk-neutral pricing arguments. Interviewers watch for clear separation of physical versus risk-neutral expectations, coherent use of equilibrium reasoning, and an ability to explain why a high-beta instrument like a call must, on average, be priced to rise over time to compensate for its risk.

What it tests

Options, as derivative securities, inherit and amplify the risk characteristics of their underlying assets, a phenomenon captured by their 'beta.' In equilibrium, assets with higher beta must offer higher expected returns to compensate for their greater systematic risk, as required by the Capital Asset Pricing Model (CAPM). For options, this means that their expected price change is not simply a function of the underlying's drift, but is scaled up by their own beta, which can be much larger than one due to leverage. The principle holds because investors demand compensation for bearing more market risk, and the market prices options so that their expected returns align with their risk exposures. This ensures that, on average, the expected price of a high-beta option like a call will increase over time, even if the underlying asset's expected return is only modestly positive.