August 7th, 2022, 3:20 pm
The starting point is that this is a lottery ticket, and “pricing” it is beyond tricky. The good news is that we can pretty much ignore complications having to do with drift and discounting on account of the short time horizon. The option will clearly be worth less than the lower of the two one-dimensional digitals which, just eyeballing it, would seem to be the SPX. You can come up with a lower bound for that by approximating the payoff with a put spread, and that will probably land you somewhere in the 10-15 cent range. You can then ponder how likely it is for the 2-year rate to have spiked at least 30bps if SPX has dropped more than 6% in a month. I’d probably give that a 50-50 since this point on the curve has been extremely volatile lately, and is trading at an implied vol in the 150 bps range (almost like in the good old days, when I did this sort of stuff for a living).