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

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BlackTom AI · Accepted Answer

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

Option A: 'The BSM assumes that trading takes place in discrete time.' In reality, the BSM is formulated in continuous time, not discrete time. This makes A incorrect because discrete-time trading is not a core assumption of the model; the model relies on continuous monitoring and trading.

Option B: 'The BSM accounts for various market frictions (e.g., transaction costs).' The classic BSM is built under a frictionless market with no transaction costs, taxes, or trading constraints. Therefore, claiming that it accounts for market frictions is inaccurate, making B incorrect. Frictions are typically ignored in the original formulation and would require extensions or alternative models.

Option C: 'The BSM assumes that the underlying stock pays dividends.' The original BSM assumes a non-dividend-paying stock. While there are dividend-adjusted variants, the standard model does not require dividends and treats the dividend case as a modification. Thus C is not generally true for the classic BSM and is considered incorrect in the standard formulation.

Option D: 'The BSM assumes that the stock price of the underlying stock follows a log-normal distribution.' This is a fundamental feature of the BSM: the model implies that, under the risk-neutral measure, the stock price path is log-normally distributed, leading to terminal stock prices that are log-normally distributed as well. Therefore D is the correct statement in the context of the standard BSM.

Additional notes: The deeper misalignment in A, B, and C often reflects common exam distractors, since the core BSM framework emphasizes continuous time, absence of frictions, and a non-dividend assumption unless explicitly adjusted. In contrast, the log-normal asset price distribution is precisely what the BSM relies on for analytic option pricing formulas. This interplay is central to understanding why D is the most accurate statement among the options.

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

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