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Hasek
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Calibration of a volatility smile model on a partial smile

February 24th, 2022, 8:43 am

I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/surface calibrated only on ITM and ATM quotes? I think that it's going to somehow underestimate/overestimate the real volatility in ITM and OTM regions. Will these effects be the same for all smile models? What if one would calibrate it on OTM and ATM without ITM? I'm looking for either quantitative or qualitative explanation.
 
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Alan
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Re: Calibration of a volatility smile model on a partial smile

February 25th, 2022, 3:48 pm

Not my area, so perhaps you can explain how both the caps and floors are (all) simultaneously ITM and that is always the case (historically). 
 
Hasek
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Re: Calibration of a volatility smile model on a partial smile

February 27th, 2022, 9:22 pm

Yeah it's probably worth elaborating on it a little bit more... So I'm talking about a market where there is only one significant market maker providing indicative quotes for caps/floors and there are usually no more than 2-3 trades made per week, so there is no opportunity to calibrate a model to real trades. The interest rate was roughly 5% and the market maker was providing quotes for 4% floors as well as ATM, 6%, 8%, 10% caps. However due to the global inflation current ATM is already set at 12-13% with fixed strikes staying the same, i.e. 6%, 8%, 10% caps are ITM and 4% floor is OTM.
 
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Alan
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Re: Calibration of a volatility smile model on a partial smile

February 28th, 2022, 2:23 pm

I see. As I said, not my area, but will make a somewhat vague suggestion anyway. Since global inflation is driving things, perhaps model that with nominal rates given in each local market as local-market-dependent spread. Other (SABR) parameters could also have local relationships. The point is that your calibrations would be done with liquid markets. Finally, use your knowledge of these (good) calibrations to just ballpark parameters that more-or-less fit your target illiquid market. 

In the last step, you might consider using an "exact" model (exact SABR, say) rather than a series expansion to make sure the target model derivative prices are arbitrage-free.
 
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doublebarrier2000
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Re: Calibration of a volatility smile model on a partial smile

September 7th, 2022, 6:33 am

try looking at short tenor swaption vols to get  feel for the parameterization