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Hasek
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Posts: 9
Joined: October 2nd, 2021, 9:53 am

Implied volatility surface of an average rate Asian caps

February 7th, 2022, 10:25 pm

Lets say I have a SABR model where implied volatility is given by semi-analytical Hagan et al. formulas and individual caplets are priced with analytical Black formulas. This model allows me to interpolate an implied volatility surface of vanilla European caps once calibrated on vanilla European caps. Suppose that I want to somehow adapt this model for the case of Asian caps, i.e. caps with every individual caplet being an Asian (average rate) option, so that I can interpolate an Asian caps volatility surface once calibrated on market quotes of Asian caps. My thoughts are
  • calibrate an existing model for vanilla European options on Asian caps to obtain SABR parameters on each volatility smile
  • use these SABR parameters to simulate the price of every Asian caplet via Monte Carlo simulation and obtain Asian caps prices as sums of constituent Asian caplets
  • quote an implied volatility of an Asian cap as an implied volatility of vanilla European cap with the same price, strike and maturity
Is there any reasoning behind my approach? Does it make sense?
 
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DavidJN
Posts: 242
Joined: July 14th, 2002, 3:00 am

Re: Implied volatility surface of an average rate Asian caps

February 8th, 2022, 4:03 pm

I’ll weigh in by stating the obvious - the volatility of the underlying should have nothing to do with the type of option being traded, the option model handles that part. I am of course assuming that the vanilla and average option models are logically consistent in the modeling sense (i.e. same assumptions).
 
To the extent that the vanilla option model is miss-specified, one implies something “more” or “different” than the pure implied volatility of the underyling from the option price. But that critique can also apply to an exotic option model that is logically consistent with the vanilla model as well.
 
It has been more than a decade since I traded options professionally, but I’ll stick my neck out and say that I’d imply volatilities from the most liquid options available on the underlying, probably European, and directly use those as inputs to an average option model.
 
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DavidJN
Posts: 242
Joined: July 14th, 2002, 3:00 am

Re: Implied volatility surface of an average rate Asian caps

February 12th, 2022, 3:38 pm

Of course also I meant to say that the liquid vol quotes would be fitted to some kind of no-arbitrage vol surface model (e,g, SVI) before being used to price exotics.