If the implied volatility surface is flat (i.e. ,all options have the same implied volatility),then

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If the implied volatility surface is flat, this means that all options have the same implied volatility. In this case, the Derman-Kani implied binomial tree coincides with the Cox-Ross-Rubinstein binomial tree. The CRR tree assumes constant volatility, whereas the Derman-Kani tree is a form of stochastic volatility model, so there may be differences between the two trees if there is variability in the implied volatility surface. However, if the implied volatility surface is flat, this source of variability is eliminated, and the two trees will be the same. Option A is incorrect because flatness of the implied volatility surface does not prevent construction of Derman-Kani trees. Option B is incorrect because the Derman-Kani tree should be able to accurately price options at all strikes, not just at-the-money options. Option D is partially correct, in that there may still be differences between the Derman-Kani and CRR trees due to the assumption of stochastic volatility in the former. However, the fact that the implied volatility surface is flat is not relevant to this.

If the Implied Volatility Surface Is Flat (I