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mrravioli
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Joined: August 4th, 2017, 5:50 am

Volatility Wing Model in ORC

August 17th, 2017, 1:12 pm

Hi guys,

I'm reading the quant manual from ORC (now part of ITIVITI) and learned the 'wing model' they use for fitting the volatility curve.
Volatility models specifics - SourceForge
https://www.google.com/url?sa=t&rct=j&q ... InuoA0I91gIt is quite simple math-wise - basically quadratic spline with smoothing and flattened parts on both sides (the 'wing' part?). 

However, I'm a bit confused about the idea and how to use this model. Why do we want our skew to flatten out on the deep ITM/OTM parts? Does that mean we would get more reasonable results when extrapolating the skew?

In addition, when fitting the wing curve, do we manually set the dc,uc,dsm,usm parameters, i.e. do we fix the ranges before fitting, or rather these are also parts of the parameter set to be optimized? It seems that, with the ORC software, I can fix, set manually and fit whatever parameter I want. I don't have the ORC software on hand so can only infer the usage from the manual. It would be really helpful if anyone who use(d) ORC could shed some light on it.

Thx in advance!
 
frolloos
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Re: Volatility Wing Model in ORC

August 17th, 2017, 2:35 pm


However, I'm a bit confused about the idea and how to use this model. Why do we want our skew to flatten out on the deep ITM/OTM parts? Does that mean we would get more reasonable results when extrapolating the skew?
What do you mean the skew flattens? At first I thought you are saying that in the model the slope of the smile (i.e. the skew) goes to zero for deep OTM / ITM options - which sounds odd. But if I read this, then it clearly states that anyhow the skew asymptotics satisfy Lee's conditions, which is fine. 

(slightly edited text above)
Last edited by frolloos on August 17th, 2017, 2:59 pm, edited 2 times in total.
 
mrravioli
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Joined: August 4th, 2017, 5:50 am

Re: Volatility Wing Model in ORC

August 17th, 2017, 2:50 pm

Yup, the slope goes to zero (skew goes constant) at the tails. I'm also confused about this setting.

I attached a plot from the manual.
Attachments
IMG_0733.JPG
 
frolloos
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Re: Volatility Wing Model in ORC

August 17th, 2017, 2:57 pm

Ok I see. Well, if I recall correctly Lee's conditions place an upper bound on the slope at the wings. So, a flat vol can still be consistent with that, even though intuitively it seems odd. It is not a setting you can change yourself? 
 
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Alan
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Re: Volatility Wing Model in ORC

August 17th, 2017, 6:21 pm

In general, ad hoc skew parameterizations (like the one in the picture) will admit butterfly arb's. 

To check a given case, insert it into BS formula and apply Breeden-Litzenberger relation to find the risk-neutral density [$]Q(K)[$], which is the density for [$]S_T = K[$] at the given option maturity [$]T[$]. 

If [$]Q(K) < 0[$] for any K>0, it's problematic. The problem is not usually the wings but the transition area. This doubt is based solely upon the posted picture; I have no other knowledge of what they are doing. 
 
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logos01
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Re: Volatility Wing Model in ORC

August 25th, 2017, 11:09 am

This parameterization is not made to be arbitrage free: at x=0 there is a discontinuity in the second derivative.