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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.
## Explanation **D is correct** because if all the BSM model assumptions hold, then all options on the same underlying asset will have the same implied volatility at all times, regardless of their time to expiration. **A is incorrect** because both the BSM model and the binomial tree approach use asset volatility computed from historical prices, not just one model using implied volatility and the other using historical volatility. **B is incorrect** because both the BSM model and the binomial tree approach use risk-neutral valuation, meaning they both assume that the expected return from the underlying asset is the risk-free rate of interest. **C is incorrect** because in the binomial tree approach, delta does not remain constant at every node through time, even though the probabilities of price movements remain constant during a given period. Delta changes as the option's moneyness changes at different nodes in the tree.
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A derivative trading firm that previously used only the Black-Scholes-Merton (BSM) model to value options has recently decided to use the binomial tree option pricing model as well. An analyst at the firm is reviewing the different features of the two models to compare and contrast their inputs and assumptions. In comparing the two models, which of the following statements is correct?
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.