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

Question

BlackTom AI · Accepted Answer

Consider the foundational assumptions of the Black-Scholes Model (BSM) as used in option pricing. 
Option A: 'The BSM assumes that trading takes place in discrete time.' This is incorrect because the BSM is built on a continuous-time framework, not discrete-time trading, allowing for continuous hedging and infinitesimal time steps in its differential equations. 
Option B: 'The BSM accounts for various market frictions (e.g., transaction costs).' In reality, the BSM abstracts away frictions such as transaction costs, bid-ask spreads, and liquidity constraints to derive a clean theoretical price; thus this statement is inaccurate. 
Option C: 'The BSM assumes that the underlying stock pays dividends.' While there are variants of the model that incorporate dividends, the standard classic BSM assumes a non-dividend-paying stock unless explicitly adjusted; as a general claim about the original model, this option is misleading. 
Option D: 'The BSM assumes that the stock price of the underlying stock follows a log-normal distribution.' This reflects a core assumption of the model: under the risk-neutral measure, the stock price process is modeled as geometric Brownian motion, which implies a log-normal distribution for prices at any future time. This characterization aligns with the mathematical structure of the BSM. 
To summarize the contrasts: A contradicts continuous-time modeling, B ignores market frictions that BSM omits by design, C is only conditionally true in extended versions but not in the standard formulation, and D directly matches the fundamental log-normal price behavior implied by geometric Brownian motion underpinning the BSM.

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

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