CHAPTER 8Volgamma, Butterfly, and Kurtosis

We began our study of smile in the previous chapter. This chapter extends our understanding of smile via study of three closely related ideas, namely volgamma, butterfly, and kurtosis.

Volgamma Volgamma describes how the images of an option varies with images. Its definition is

(8.1)images

Recall from Equation (5.3) that images is independent of images for an ATM option and hence its volgamma is zero. However, I show ahead that a long position in an OTM option is long volgamma.

From the previous definition we see that a trader with a long volgamma position, images, derives longer images when images rises. If she wishes to return her to its previous level, then she can sell options. She may be ...

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