No abstract

We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for numerically efficient calibration of the model.

We show two examples of operators acting on some Hilbert space and having invariant domains: a paranormal operator, which is not closable and a paranormal and closable operator, which closure is not paranormal. We start by establishing some general lemmas and propositions associating the families of operators mentioned above.

We show that if an operator-valued analytic function f of a complex variable attains its maximum modulus at z0, then the coefficients of the nonconstant terms in the power series expansion about z0 cannot be invertible, provided a complex uniform convexity condition holds. One application is that the norm of the resolvent of an operator on a complex uniformly convex space cannot have a local maximum. Mathematics Subject Classification (2010). Primary 32A10;Secondary 30C80, 46E40.