CHAPTER 7Vanna, Risk Reversal, and Skewness

In the previous chapter I discussed that traders use the BSM function to value options by defining images such that images. This chapter focuses on a serious shortcoming of this approach; it is not in general possible to use the same value of images to price options of two different strikes on a particular expiry date.

Traders adjust for this shortcoming using smile. Smile refers to the fact that the value of images that must be inserted into images to match the prices of traded options is not constant across different strikes. For example, a 1‐year expiry OTM put may trade with a higher images than the ATM strike. That is, images is made a function of strike and one must write images. The function ...

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