Thread by @samchepal

#BTC daily returns are not normal! After running a Gaussian kernel density estimation and comparing this to its respective normal distribution, we can see that #BTC has a lot of kurtosis as shown by the "peakedness" near the centre.

Also, Black Thursday and other extreme events occur much more often than a normal distribution would predict. This can be seen in the weight of the tails of the estimated distribution.

Theoretically, if the market is pricing in a normal dist the trader can make money here.

As a recap, the estimated dist has a greater probability of staying in the centre than the normal dist would predict. Also, the estimated dist has fatter tails than the normal dist.

The trader could short an ATM straddle and buy an OTM strangle. The estimated dist suggests that returns are more likely to stay near zero, hence we can sell vol here. However, buying the OTM strangle will give us exposure to outsized moves in the underpriced tails.

A key point - we remain vega neutral in this trade at inception by having a larger notional for our strangle leg than our straddle leg...

This is because the ATM straddle has higher vega than the strangle using OTM options. Selling/buying the straddle/strangle respectively in equal notional would result in a negative vega position. As a result, we need to increase the notional of the strangle to stay vega neutral.

I came across this concept after reading @asiqbal's excellent book on options pricing theory. For this analysis I used #BTC daily data from 2014-09-18 to 2020-09-17.

I'd love to learn how others model the distributions of asset returns to trade vol.