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Jericho
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Posts: 20
Joined: August 22nd, 2007, 3:14 pm

Dual hybrid option

August 7th, 2022, 8:25 am

Hi i want to price a dual hybrid option where I receive a payout in 1M if S&P < 3900 and 2yr SOFR IS more than 3.5% at expiry.

Rather than go into bbg and price this up is there a more intuitive way to price this or think about this or approximate this? Can i decompose into its constituent parts and approximate a price? Any useful comments would be appreciated thks
 
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bearish
Posts: 4877
Joined: February 3rd, 2011, 2:19 pm

Re: Dual hybrid option

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).
 
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Jericho
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Posts: 20
Joined: August 22nd, 2007, 3:14 pm

Re: Dual hybrid option

August 7th, 2022, 6:52 pm

Thank you Bearish always good to learn from you. Just want to clarify a couple things, how did you calculate the 10-15 % range for the s&p through the put spread. And then you are multiplying this by 50% so as to imply a price of 5% to 7.5%?
 
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bearish
Posts: 4877
Joined: February 3rd, 2011, 2:19 pm

Re: Dual hybrid option

August 7th, 2022, 8:57 pm

To be honest, I just eyeballed the implied vol at that strike in the low 20’s and figured the skew was going to work against you. I did not actually do the real calculation, although I don’t think that should be too hard. And then, yes, I think it is appropriate to apply a haircut of sorts to account for the fact that you also need the 2-year swap rate to rise. If this were my money, on a reasonable scale, I’d be inclined to bid about 5%.