Answer-first summary for fast verification
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.
D is correct. If all the BSM model assumptions hold, then all options on the same underlying asset will have the same implied volatility at all times. A is incorrect. Both the BSM model and the binomial tree approach use asset volatility computed from historical prices. B is incorrect. Both the BSM model and the binomial tree approach use the risk-neutral valuation, that is, assume that the expected return from the underlying asset is the risk-free rate of interest. C is incorrect. In the binomial tree approach, delta does not remain constant at every node (through time) even though the approach takes the probability of the price moving up and the probability of the price moving down not to change during a given period.
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A firm that focuses on derivatives trading has traditionally used the Black-Scholes-Merton (BSM) model for option valuation. Recently, the firm decided to add the binomial tree option pricing model to its set of analytical tools. A financial analyst at the firm is now comparing the two models to understand their different features, inputs, and underlying assumptions. In evaluating these models, which of the following statements provides an accurate comparison of their characteristics?
A
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.