Interest rate spreads implicit in options: Spain and Italy against Germany

The options premiums are frequently used to obtain probability density functions (pdfs) for the prices of the underlying assets. When these assets are bank deposits or notional Government bonds it is possible to compute probability measures of future interest rates. Recently, in the literature there have been many papers presenting methods of how to estimate pdfs from options premiums. Nevertheless, as far as we know, the estimation of probabilities of forward interest rate functions is an issue that has not been analysed before. In this paper, we propose such a method, that can be used to study the evolution of the expectations about interest rate convergence. We look at the cases of Spain and Italy against Germany, before the adoption of a single currency, and conclude that the expectations on the short-term interest rates convergence of Spain and Italy vis-a-vis Germany had a somewhat different trajectory, with higher expectations of convergence for Spain.