Which of the following statements about the Black-Scholes Model (BSM) is most likely true?

Question

BlackTom AI · Accepted Answer

The question asks about the Black-Scholes Model (BSM) and which statement is most likely true.

Given option: D. The BSM assumes that the stock price of the underlying stock follows a log-normal distribution.

To analyze this, recall core BSM assumptions: the underlying asset price follows a geometric Brownian motion with constant drift and volatility, which implies that the logarithm of the price is normally distributed. Consequently, the price itself is log-normally distributed at any future time. This is a fundamental feature of the model and underpins the closed-form Black-Scholes formula for option pricing.

Why this statement is consistent with BSM: the log-normal distribution of S_t arises from the stochastic differential equation dS_t = μS_t dt + σS_t dW_t, which leads to S_t having a lognormal distribution when viewed over a finite horizon. Under the risk-neutral measure used for pricing, the drift term becomes the risk-free rate, but the lognormal nature of the distribution remains.

Why someone might doubt this: if one misremembers and thinks the model assumes normal (not log-normal) distribution of prices, that would be incorrect. The BSM does not assume a normal distribution for prices themselves; it is the log-prices (log S_t) that are normally distributed under geometric Brownian motion, yielding S_t as log-normal. Some discussions may talk about approximation issues or deviations in real markets, but the idealized BSM framework indeed yields a log-normal stock price distribution.

In the absence of other options to compare against, this statement is a precise description of a standard BSM property and aligns with the theoretical derivation and practical pricing formula associated with the model.

Which of the following statements about the Black-Scholes Model (BSM) is most likely true?

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