Thread by @KrisAbdelmessih

An example of why weekly vol is more volatile

Suppose 5 day option. Stock daily vol is 1% per day.

IV = sqrt(.01² x 5 days x 52 weeks) = 16.1%

Ok say 1 day is now expected to be 3% daily vol

IV = sqrt([.01² x 4 days + .03² x 1 day] x 52 weeks) = 26%

What happened?

https://twitter.com/KrisAbdelmessih/status/1380970956580028416

The single day expected vol jumping from 1% to 3% means there is more variance in that single day then the remaining 4 days!

.01² x 4 days < .03²

For a longer dated option the increased vol from a single day (like earnings) is clearly diluted...

If the option had 2 weeks to expiry:

IV sqrt([.01² x 9 days + .03² x 1 day] x 52 weeks) = 21.6%

1 month:

IV sqrt([.01² x 21 days + .03² x 1 day] x 12 months) = 19%

So let's recap what happened when we inserted a single day of 3% vol to understand the risk...

The 1 week option vol went from 16% to 26%. 10 vol point increase

The 1 month option went from 16% to 19%. 3 vol point increase.

But...

The vega of the 1 month option is 2x the vega of a 1 week option.

So what is the net p/l effect...

The near dated straddle increased by 10 points x the vega

The 1 month straddle increased by 3 points x 2 x the vega of the near dated straddle

10/6 = 1.66

The near dated straddle increased in price 66% more than the 1 month straddle!

This is why event pricing is so important!