An option-trading firm is using the Black-Scholes (1973) model to price their options using the same level of volatility for all strikes. The market anticipation is that sharp negative gapping behavior is likely given that sudden recessionary information is being released in spurts. By using the Black-Scholes model with a constant volatility the firm is
A) Underpricing out-of-the-money calls relative to in-the-money puts.
B) Underpricing out-of-the-money puts relative to in-the-money calls.
C) Underpricing out-of-the-money puts and in-the-money puts relative to those at-the-money.
D) Underpricing out-of-the-money puts relative to those at-the-money.

Question

Quizplus · Accepted Answer

The constant volatility assumption used by the firm would lead to an underestimation of the implied volatility for out-of-the-money puts relative to those that are at-the-money. This is because Black-Scholes assumes that the implied volatility is constant for all strikes, but in reality, the implied volatility is higher for out-of-the-money options when the market anticipates sharp negative gapping behavior. Therefore, the firm would be underpricing the out-of-the-money puts relative to those that are at-the-money.

An Option-Trading Firm Is Using the Black-Scholes (1973) Model to Price