Variance Optimal Cap Pricing Models.

We propose new closed-form pricing formulas for interest rate options which guarantee perfect compatibility with volatility smiles. These cap pricing formulas are computed under variance optimal measures in the framework of the market model or the Gaussian model and achieve an exact calibration of observed market prices. They are presented in a general setting allowing to stud model and numeraire choice effects on the computed prices. Numeraire dependence is particularly emphasized. A numerical example and an empirical application on market data are given to illustrate the practical use of the calibration procedure.