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Samsaveel
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Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Capturing skew risk in IV swaption surface in VaR Framework

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?

Samsaveel
Topic Author
Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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: 3256
Joined: July 18th, 2006, 5:49 am

### Capturing skew risk in IV swaption surface in VaR Framework

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...

Samsaveel
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Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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: 3256
Joined: July 18th, 2006, 5:49 am

### Capturing skew risk in IV swaption surface in VaR Framework

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

Diskiss
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Joined: September 28th, 2004, 8:51 am

### Capturing skew risk in IV swaption surface in VaR Framework

Samsaveel
Topic Author
Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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

pcaspers
Posts: 700
Joined: June 6th, 2005, 9:49 am

### Capturing skew risk in IV swaption surface in VaR Framework

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 ?

Samsaveel
Topic Author
Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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 ?

pcaspers
Posts: 700
Joined: June 6th, 2005, 9:49 am

### Capturing skew risk in IV swaption surface in VaR Framework

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.

Samsaveel
Topic Author
Posts: 436
Joined: April 20th, 2008, 5:47 am

### Capturing skew risk in IV swaption surface in VaR Framework

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