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Explanation:
Explanation: C is correct. The derivation of the Black-Scholes-Merton model (BSM) assumed that there are no riskless arbitrage opportunities. This no-arbitrage argument is at the heart of the derivation and, unlike other BSM assumptions, cannot be relaxed under extensions of the original model.
A is incorrect. The BSM formulas have been adapted for use with options on stocks that pay dividends, either through discrete dividend payments or a continuous dividend yield.
B is incorrect. This is a misstatement of an assumption under BSM; it is actually assumed that options cannot be exercised early. American options allow for early exercise, but it can be shown that for American call options on stocks with no dividends or sufficiently small dividends, early exercise is never optimal. BSM can therefore be used for these options by assuming they are European.
D is incorrect. Among the assumptions necessary to derive BSM, the return from a non-dividend paying stock over a short period of time is assumed to be normally distributed. However, when this is true, the stock price at the end of a relatively long period follows a lognormal, not normal, distribution.
Learning Objective: Describe the assumptions underlying the Black-Scholes-Merton option pricing model.
Reference: Global Association of Risk Professionals. Valuation and Risk Models. New York, NY: Pearson, 2023. Chapter 15. The Black-Scholes-Merton Model [VRM-15]
Q-100. A trader on the options trading desk at an investment bank is discussing the Black-Scholes-Merton model with an intern. The trader mentions that while various assumptions were used to originally derive the model, several of those assumptions have been subsequently relaxed to allow for the pricing of options under a wider array of circumstances. However, the trader stresses that some other assumptions have not been relaxed and are still considered necessary. Which of the following assumptions is necessary for the Black-Scholes-Merton model to be used in pricing options?
A
The underlying asset does not pay any dividends during the life of the option.
B
The option under consideration cannot be an American option.
C
The execution of risk-free arbitrage opportunities is not possible.
D
The underlying asset's price at the end of a 1-year period will be normally distributed.
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