# Why is the right part of the vol smile referred to as call skew

I often see the right part of the vol smile referred to as 'call skew'. However, due to put/call parity, this also represents skew for ITM puts. Is there a reason behind this convention?

• To simplify and answer your question, the right part is referred as call skew because the implied vol comes from OTM call options. Similarly, the left part comes from OTM put options. @LocalVolatility has put a thorough answer already for why this is the case. As a side note, the lowest point of the smile is often not ATM or ATMf. That's why there is an additional term called ATM skew. – Will Gu Dec 9 '16 at 17:43

I am not familiar with the terms call and put skew but rather upside and downside skew. However, I can image why they are used by some people.

$$s(T, K) = \alpha \frac{\partial V}{\partial \sigma}(T, K) + \beta \left| \frac{\partial V}{\partial S}(T, K) \right|.$$
Here, $\alpha$ is the spread you charge for one unit of vega and $\beta$ is the spread you charge for one unit of delta. Since the vega of European call and put options of the same strike are identical the spread difference stems from the delta. Since out-of-the-money options have a lower absolute delta, you are showing tighter quotes for them.