All the inputs in the Black-Scholes option pricing model are directly observable except

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In this question about the Black–Scholes option pricing model, we evaluate which inputs are directly observable versus inferred.
Option a: the price of the underlying security. The current price of the underlying asset is a market quote that is readily observable in real time. This input is clearly observable, so this option is not the correct choice for the exception.
Option b: the risk-free rate of interest. The risk-free rate (usually the yield on government securities) is published by financial data sources and is observable to market participants. While it can be proxied by different maturities, it remains an observable parameter, so this option does not represent the non-observable input.
Option c: the time to expiration. The time to expiration is determined by the option’s contractual terms and the current date, which makes it directly known to traders and observable in practice. This is not the non-observable input.
Option d: the variance of the underlying asset. The true annualized volatility (variance) of the underlying is not directly observable in the market. Traders must estimate it from historical prices or infer it from option prices (implied volatility). This makes variance the input that is not directly observable, i.e., the exception in the statement.
Option e: the strike price. The strike price is fixed in the contract terms and is a known, observable quantity at initiation and throughout the option’s life. This is directly observable, so it cannot be the exception.
Therefore, the only input that is not directly observable is the variance of the underlying asset, while the other inputs are observable or predetermined by the contract or market data.

FINS3635-Options, Futures & Risk Mgmt - T3 2025

All the inputs in the Black-Scholes option pricing model are directly observable except

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