Swaption Greeks?

When considering Dv01, gamma, etc. what is considered the "underlying"? I see the DV01 is negative for payers, so surely the underlying isn't the forward rate?

Also, should DV01 be seen as roughly equal to Probability(of expiring in the money) * Annuity PV01 for the resulting swap?

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why wouldnt the underlying be the forward rate? you can barf up a lot of math to try to prove this. e.g. you decompose ur swap rate as a weighted average of the individual forward rfr rates, call it S(t). So by construction you have to take the greeks wrt S(t). a swaption gives you the right to enter an entire fixed-for-float swap or again many forwards, so you treat the composite break-even rate as the traded "asset" if you want to think of it that way. 

in Black's world, yes. swaption dv01 \approx P(ITM) * annunity. but i wouldnt say that delta is P(ITM) or P(Exercise) see more here: https://quant.stackexchange.com/questions/31993/bachelier-option-delta-probability-of-exercise

 

Ah I see, I’ve never seen it be explained as a weighted avg before.

I’m still abit confused though due to the sign of the DV01. Just at a very basic leveled think that the value of a payer should increase if S(t) (in ur interpretation) increases,causing a positive DV01.

Is the negative sign seen on the bbg screen and bofa vol primer etc. due to the standard convention of omitting the negative sign for the DV01 for standard bonds (since it’s obvious their price decreases), so they assign a negative DV01 to draw attention to the fact that the payer will increase in value with a higher S(t)?

Another unrelated question: what is it about the SABR process that makes it more appropriate for modeling the smile for non-linear rates products compared to e.g. the Heston process? Is it due to the beta offering a mix between Normal and Log N? In my basic understanding you could technically calibrate a Heston process to fit the smile for a swaption as well?

Do you have any book recs for Rates vol? Something similar to the FX derivatives trader school book but for rates instead?

 

fwd rates are building blocks

yeah, i think dv01 sign is just convention: negative if you buy a payer, pos if you buy a receiver. 

SABR gives you closed form solutions vs having to use a pde solver/finite differencing for heston. but honestly that doesnt really matter now since theres all the different variations of approximate/semi analytical heston. also pricers now use auto diff to solve the pdes so you probably wont notice a huge difference in speed with what gets spits out.

this is thread will be more helpful: https://quant.stackexchange.com/questions/65872/sabr-vs-heston-for-ir-swaptions

id say reading the Hagan papers is more than enough math and should cover all the theory you need. reading sell side research/trade ideas is super helpful imo - you should follow matt kessel on LinkedIn he posts screen grabs from different banks/bbg/riskval. then messing around with Quantlib e.g. building a simple pricer, calcing the greeks, calibrating sabr, plotting the grid/smile will teach much more than a textbook

 

If you buy a payer swaption, your dv01 should be positive because the value of your position increases as the underlying swap rate increases. In rates lingo, you are 'short' rates because people refer to 'long'/'short' positions in cash instruments (bonds/swaps), but dv01 is positive.

 

that’s untrue it’s typically understood that you’re long rated in that you’re long cash prices and long the rally. receiver = long

 

I just checked as well. They aren’t defining DV01 how it is typically, they are flipping it. Just think about what you are doing if you are long a payer swaption, you own the right to pay fixed at a certain rate. Rates go up, your position increases in value, therefore positive delta. Keep in mind DV01 is used more for linear products and swaptions are not linear so delta is preferred. Additionally just think fundamentally, you own this so you have a greater than 0 probability of receiving a payer swaption at delivery, if I pay fixed I’m always long 01s, so if there is any chance I end up with the right to pay fixed then I am (proabability it happens) x (DV01 of that position).

 

You’re right in the traditional sense. I’m mostly in non linear land and hedge very little with cash, therefore in my head when I talk about rates in the above what I’m really talking about are the underlyings, aka swaps and their respective 01s. I also wrote the above pretty quickly so wasn’t really putting a lot of thought into how others would interpret.

 

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