Answer-first summary for fast verification
Answer: The interest rate changes randomly over time.
## Explanation The Black-Scholes-Merton model makes several key assumptions: - **Option A is an assumption**: The model assumes the underlying asset price follows a geometric Brownian motion with continuous price movements. - **Option B is NOT an assumption**: The Black-Scholes model assumes that the **risk-free interest rate is constant and known**, not that it changes randomly over time. This is one of the limitations of the original model. - **Option C is an assumption**: The model assumes constant volatility (instantaneous variance) over the option's life. - **Option D is an assumption**: The model assumes perfect markets with no transaction costs, no taxes, continuous trading, and the ability to short sell. Therefore, option B describes a condition that contradicts the Black-Scholes assumptions, making it the correct answer.
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Which of the following is not an assumption of the Black-Scholes options pricing model?
A
The price of the underlying moves in a continuous fashion.
B
The interest rate changes randomly over time.
C
The instantaneous variance of the return of the underlying is constant.
D
Markets are perfect, i.e., short sales are allowed, there are no transaction costs or taxes, and markets operate continuously.
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