Short Option Skewness

[fullofquestions]

I was recently going over chapter four of the FRM handbook when I came across the statement, "Relative to a symmetric distribution, a short option position has negative skewness, or a long left tail," on page 100. Example 4.9 also states matter of fact, that "short option positions have long left tails."

I was under the impression that a long call has a right tail. A short call also has a right tail although the right tail at some point would cross the x-axis and go negative.

For puts, I believe a long put has a left tail, whereas a short put also has a left tail although at some point the tail would go negative.

Would anyone care to comment? Much appreciated.

 

[southeuro]

any answers would be appreciated. Thanks

 

[ShaktiRathore]

a short put option has payoff = premium-max(X-St,0) so that losses increases when the stock price moves down due to degree of loss aversion the investors panic when price goes down and thus would result in more losses than anticipated because all investors would take out their money leading to huge losses and long left tail for short puts. Thus there is negative skewness that can come in to the picture due to asymmetric distribution of returns to short put position. On the positive side the short put pays a premium while on the negative side the irrational behavior of investor can cause negative skewness.

thanks