Effect of Skew on Delta

The skew curve of a particular stock can have a big impact on a trader's delta hedge against any option positions he has. 



Trader is long 1Y Call 120% on a stock. 

Skew curve for the 1Y maturity indicates that every 10% decrease in strike translates into a 1.5% increase in IV. 

So if ATM vol = 20% --> 120% IV = 17%. 


Suppose instead that the trader decides to mark this 120% IV at 21% --> smile. 

Because of that, his delta is larger than it should be (think intuitively at the proba to be ITM) --> the trader sells more shares than he should. 


The way a trader marks his IV surface has a large impact on his delta hedge. 


So the trader assignes too high a probability of the option expiring ITM and hedges the upside call on too high a delta. 

To make matters worse, he will continue to sell too many shares with the spot increasing.

With the spot increasing, the stock is likely to realise even less, making the probability and therefore the proper delta of this option even lower. 


CCL: by marking upside strikes on a higher IV than ATM IV, the trader sells too many shares, and especially when S increases, the trader not only loses money on extra shares he sold, but he also continues to sell too many shares. 


It is these dynamics that force a trader to mark his IV surface per maturity with a skew that has a downward sloping shape rather than a smile. 

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