Is volatility skew proportional to the ATM volatility of the underlying

Quick glance,it certainly appears that way, doesnt it??
Keep in mind,its a quiet low vol market and I am guessing implied correlation is low


Is there more skew in a product like SPY OTM puts than a stock like TSLA OTM puts?
 
We use delta to normalize the measurement of skew or what we call slope.
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At-the-money volatility is the implied volatility at the 50 delta call and put. Strike Slope is a measure of the amount that implied volatility changes for every increase of 10 call delta points within the intra-month skew. It measures how lopsided the 'smile' or 'smirk' is. The derivative is a measure of the rate at which the strike slope changes for every increase of 10 call delta points within the intra-month skew. It measures the curvature of the intra-month skew or 'smile.' We chose just two parameters to describe the skew to get a reasonable fit for the fewest assumptions.
 
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