Most Major Stock Indices,like the S&P 500,exhibit an Implied Volatility $P \left( K _ { 1 } \right) , P \left( K _ { 2 } \right) , P \left( K _ { 3 } \right)$

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) $\sigma _ { 1 } > \sigma _ { 2 } > \sigma _ { 3 }$
)

Correct Answer:

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