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Option smile and skew in < 5 tweets. Imagine a Black-Scholes world, except that realized vol will be either 20% or 40% with 50/50 chance. Then option prices should be the average of the Black-Scholes prices in each scenario.pic.twitter.com/9ZuLoWnciy
You can calculate the implied vol for these prices, which has a smile. Near at the money the 20% and 40% vol scenarios both contribute to the price, but in the wings all of the value comes from the 40% scenario. Implied vol smile is due to unknown future volatility (vol of vol)pic.twitter.com/25Pp91iW1q
What if there is a correlation between volatility and spot? We can assume a 20% upward price drift in the low vol scenario, and a -20% drift in the high vol scenario, leading lower call prices and higher puts (blue line is previous scenario, for comparison)pic.twitter.com/xy50xXsIgR
Calculating implied vol for these prices shows both a skew and a smile - the skew comes from the negative correlation between volatility and prices. Markets with a positive correlation (like natural gas) have a skew in the opposite direction, with calls more expensive than puts.pic.twitter.com/V7bvxeNu6w
Hi, please find the unroll here: Option smile and skew in < 5 tweets. Imagine a Black-Scholes world… https://threadreaderapp.com/thread/1446044738508009474.html … Share this if you think it's interesting. 
"in 5 tweets...'
Good stuff macroCephalopod
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