If the implied volatility surface is flat (i.e., all options have the same implied volatility), then
A) Derman-Kani implied binomial trees cannot be constructed because of the lack of variability in the data.
B) The Derman-Kani tree may price away-from-the-money options inaccurately.
C) The Derman-Kani implied binomial tree coincides with the Cox-Ross-Rubinstein binomial tree.
D) The Derman-Kani implied binomial tree may still differ from the Cox-Ross-Rubinstein (CRR) tree because implied binomial trees are a form of stochastic volatility models whereas CRR trees assume constant volatility.

Question

Quizplus · Accepted Answer

If the implied volatility surface is flat, this means that all options have the same implied volatility, so there is no variability in the data. With no variability, the Derman-Kani implied binomial tree and the Cox-Ross-Rubinstein binomial tree will coincide, and the Derman-Kani tree will price options accurately. Option A is incorrect because the lack of variability in the data does not prevent the construction of Derman-Kani implied binomial trees. Option B is incorrect because a flat implied volatility surface will not affect the pricing of out-of-the-money options more than in-the-money options. Option D is incorrect because both the Cox-Ross-Rubinstein tree and the Derman-Kani tree make assumptions about volatility, with the Derman-Kani tree being a form of stochastic volatility model.

If the Implied Volatility Surface Is Flat (I