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?