Most major stock indices, like the S&P 500, exhibit an implied volatility skew. This means if we consider three put options, $P \left( K _ { 1 } \right) , P \left( K _ { 2 } \right) , P \left( K _ { 3 } \right)$ at strikes $K _ { 1 }

Question

Most major stock indices, like the S&P 500, exhibit an implied volatility skew. This means if we consider three put options, $P \left( K _ { 1 } \right) , P \left( K _ { 2 } \right) , P \left( K _ { 3 } \right)$ at strikes $K _ { 1 } < K _ { 2 } < K _ { 3 } \leq S$ (where $S$ is the current index level) and the options have implied volatilities $\sigma _ { 1 } , \sigma _ { 2 } , \sigma _ { 3 }$ , respectively, then the most likely pattern is A) $\sigma _ { 1 } < \sigma _ { 2 } < \sigma _ { 3 }$ . B) $\sigma _ { 1 } = \sigma _ { 2 } < \sigma _ { 3 }$ . C) $\sigma _ { 1 } = \sigma _ { 2 } = \sigma _ { 3 }$ . D) $\sigma _ { 1 } > \sigma _ { 2 } > \sigma _ { 3 }$ .

Quizplus · Accepted Answer

The implied volatility skew means that options with lower strike prices (further out of the money) tend to have higher implied volatilities than those closer to the current index level. This is because there is often more fear or uncertainty about significant market drops, leading to higher premiums for out-of-the-money puts. Therefore, as the strike price decreases ($K_1 < K_2 < K_3$), the implied volatility increases ($\sigma_1 > \sigma_2 > \sigma_3$).

Most Major Stock Indices, Like the S&P 500, Exhibit an Implied