Financial Risk Manager Part 1
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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 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?
Explanation:
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.