first time -I'm curious as to how the following would work:
I have a 2 day(only includes full day of Thursday and Friday) swaption with a volatility of 100 bps.
We also know the weights we've assigned for the next 2 days, i.e thursday has a weight of 2(we multiply the daily bp vol by 2 - this can be due to a market event causing rates to move - i.e Fed meeting), and Friday is just a standard weight of 1.
How would we go about finding the daily bp vol breakeven for Thursday and Friday.
I tried the following but am uncertain if it is correct, because it may not be a linear interpolation:
100/(sqrt(252) =6.2599 avg daily bp vol
2x + x = 2*(6.299) - multiply by 2 because 2 biz days
x= 4.1966(fridays vol; Annualized: 66.67)
2x = 8.399 (thursdays vol; Annualized: 133.33)