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Answer: If the assumptions of the BSM model hold, the implied volatility of a longer-term option and the implied volatility of a shorter-term option on the same underlying asset will be the same.
The correct answer is D. If all the assumptions of the Black-Scholes-Merton (BSM) model hold, then all options on the same underlying asset will have the same implied volatility at all times. This is because the BSM model assumes a constant volatility for the life of the option, which is reflected in the implied volatility used as an input to the model. Option A is incorrect because both the BSM model and the binomial tree approach use asset volatility computed from historical prices, not just implied volatility for the BSM model and historical volatility for the binomial tree. Option B is incorrect because both models use the risk-neutral valuation approach, which assumes that the expected return from the underlying asset is the risk-free rate of interest, not just the binomial tree approach. Option C is incorrect because in the binomial tree approach, delta does not remain constant at every node. Although the probabilities of the price moving up and down do not change during a given period, delta can still vary at each node due to the changing option values as the tree progresses.
Author: LeetQuiz Editorial Team
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A firm, which had previously relied exclusively on the Black-Scholes-Merton (BSM) model for the valuation of options, has now opted to incorporate the binomial tree option pricing model into its valuation toolkit. An analyst at the firm is tasked with examining the unique characteristics of these two models in order to evaluate and contrast their parameters and assumptions. In making this comparison between the BSM model and the binomial tree model, which of the following statements is accurate?
A
1 The BSM model uses an underlying asset's implied volatility as an input but the binomial tree approach uses its historical volatility.
B
The binomial tree approach, but not the BSM model, assumes that the expected return from the underlying asset is the risk-free rate of interest.
C
In the binomial tree approach, delta is equal at each node since the probabilities of the price moving up or down during a period are constant and equal for both the underlying asset and the option.
D
If the assumptions of the BSM model hold, the implied volatility of a longer-term option and the implied volatility of a shorter-term option on the same underlying asset will be the same.