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. 
First, we recall the core assumption of BSM regarding the dynamics of the underlying stock price: it is modeled as a geometric Brownian motion, which implies that the logarithm of the stock price is normally distributed. Consequently, the stock price itself has a log-normal distribution at any future time. 
Option-related consideration: since the provided data for answer options is missing, we cannot evaluate alternative statements or compare them to the standard BSM framework. 
Focusing on the standard result, the statement that the stock price follows a log-normal distribution is consistent with the fundamental BSM assumptions about price paths and the distributional properties of returns. This aligns with the established theory that under the BSM framework, S(t) = S(0) exp[(μ − 0.5σ^2)t + σW(t)], where W(t) is a Brownian motion, which yields a log-normal distribution for S(t).
In contrast, statements claiming only normal distribution of prices, or other distributions, would conflict with the log-normal consequence of geometric Brownian motion. Additionally, any claim that the model ignores volatility clustering or assumes deterministic paths would be at odds with the stochastic volatility implicit in the BSM via the diffusion term σW(t).
Given that the only option available states a log-normal distribution for the stock price under BSM, this aligns with the standard theoretical result, while the absence of other options prevents a comparative analysis of alternative claims.

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

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