CHAPTER 7Vanna, Risk Reversal, and Skewness
In the previous chapter I discussed that traders use the BSM function to value options by defining 
such that 
. This chapter focuses on a serious shortcoming of this approach; it is not in general possible to use the same value of 
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 
that must be inserted into 
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 
than the ATM strike. That is, 
is made a function of strike and one must write 
. The function ...
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