Guy'sany input on this from ,**EXPERIENCE**,articles,papers ,etc..... Thanks,

- Martinghoul
**Posts:**3255**Joined:**

I have no idea what you're asking... Surely, there is historical data for skew, just like there is for any other mkt input. That should make things relatively straightforward, no?

yeah.... no idea about the question,i guess it is relatively ill posed from a content perspective what is industry practice to determine non ATM swaption vols ,how to link the smile shape in caplet data to swaption vols all of this is in the context of HS VaR ?

- Martinghoul
**Posts:**3255**Joined:**

Again, there's all sorts of methodologies that exist for non-ATM swaption vols. You can interpolate to your heart's content, you can use SABR or another model w/whatever set of parameters you like, etc etc etc...I am not really sure why you'd want to link caplet vol/skew to swaption vol/skew. If you wanted to do so, this wouldn't be a trivial exercise by any means.I am not at all sure how all of these are specifically related to VAR. Essentially, once you have chosen your model/methodology and have generated the historical data, your VAR process should be agnostic.My Z$2c...

thanks Martingoul.a position in a swaption 10y10y starting sometime in the past,is the 10 y par swap rate used for fair valuation purposes daily ?

- Martinghoul
**Posts:**3255**Joined:**

No, you would use the appropriate fwd rate...

you should link your caplet skew to your swaption skew. Your caplet vols are essentially the "first collumn" of your swaption vols. its the 3m underlying. (if we are talking about 3m caplets). you then follow with 1y 2y.. underlying swaption data.Your capfloor skew should therefore be in line with your swaption 1y underlying skew. The most common way to model your IR skew these days is to use SABR or a variant of it. its fairly easy to calibrate and has, from a market risk perspective, a great advantage of being easily used for "proxying". Meaning if you dont have skew data for MYR skew for example but your trading desk had that great idea to sell that MYR 5y10y 100 payer to a client and your are now stuck with including it in your VaR, using your SABR parameters from your already calibrated SGD or USD if thats all you have would be a good starting point until your trading desk provides you with a better set of parameters. You would of course use the right forward and get a set of logvols derived from SABR that you can easily upload in your system.Unfortunately not many system take SABR parameters as direct inputs...

"a set of logvols derived from SABR " ,which set would that be for the USD 5y10y 100 payer ?

I understood the original question as how to capture the smile risk, which has not been answeredE.g. if you use a SABR surface and suppose you use a naive historical VaR approach, would you just calculate scenarios based on the current [$](\alpha, \beta, \nu, \rho)[$] and stress these with historical relative (?) day to day changes ?Or would you go for a more geometric approach, looking at risk reversals and butterflies and stress these two smile characteristics ?Or something else ?

QuoteOriginally posted by: pcaspersI understood the original question as how to capture the smile risk, which has not been answeredE.g. if you use a SABR surface and suppose you use a naive historical VaR approach, would you just calculate scenarios based on the current [$](\alpha, \beta, \nu, \rho)[$] and stress these with historical relative (?) day to day changes ?Or would you go for a more geometric approach, looking at risk reversals and butterflies and stress these two smile characteristics ?Or something else ?Thanks Pcaspers...how would you calculate scenarios on the current calibrated parameters [$](\alpha ,\beta,\nu,\rho)[$] ? could you shed some light on your last geometric approach ,looking at RR,BF and stressing these ?

I don't know, maybe calculate relative daily changes in alpha, bet, nu, rho and stress your current SABR parameters with these ? But I think (I did not try that), that wouldn't work, it would give non sensical scenarios. But I don't know really.

what is market practice for checking the non-arbitragability of the IR volatility surface, after adding additive perturbations for scenario generation ?

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