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Vol_Curve_FunctionsFunction Create Implied Vol Table within Vol Curve returns a Table object containing the implied volatility surface (or cube) corresponding to the given set of tradables and target prices.
For options other than swaptions, the returned implied vols span the option expiries and strikes of the input options and are therefore represented by a Table2D
For swaptions, the returned implied vols generally span the option expiries, underlying swap tenors and strikes and are therefore represented by a 3-dimensional HyperTable
Note the swaption implied vols are reported in the same format that a 3-dimensional vol table must have when used as input in the pricing of swaptions, i.e. the strikes are expressed as atm swap rate spreads and the otm vols as atm vol spreads.
In the special case where the input options are all at-the-money, the returned implied vols span only the option expiries and underlying swap tenors and are therefore represented by a Table2D
For all kinds of options, the returned vols are such, that if they were to be fed to the valuation algorithm described below, then the result would be option prices that match the provided target prices.
The valuation algorithm utilized by QuantLib depends on the option's exercise type.
All european options are priced through the analytic Black Scholes Merton model.
Non-european options are priced through the Finite Differences Crank Nicolson method, with the exception of non-european swaptions for which no implied vol can be calculated.
Note the volatility matrix elements that do not correspond to the provided options are filled using linear interpolation and flat extrapolation.