Wednesday, October 24, 2012

skew bump on a smile curve

Background -- in volatility smile (rather than term structure) analysis, we often use a number (say, -2.1212) to measure the skewness of a given smile curve. Skew is one of several parameters in a calibrated formula that determines the exact shape of a given smile curve. Along with anchor volatility, skew is among the most important parameters in a parameterization scheme.

We often want to bump the skew value (say by 0.0001) and see how the smile changes.

A bump in skew would make the smile curve Steeper at the ATM point on the curve. You need to look at both the put (low strike) and call (high strike) sides of the smile curve. If the bump causes put side to move even higher and call side to move even lower, then skewness is further increased. In many cases, skew value of the entire curve is (approximately?) equal to the slope (first derivative) at the ATM point.

If you mistakenly look at only one side of the smile curve, say the put side, you might notice the curve flattening out when skew is bumped. Entire left half may become less steep, while the right half was rather flat to start with. So you may feel both halves become less steep when skew is bumped. That's misleading!

Note skew is usually negative for equities. A bump is a bump in the magnitude.

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