Calibration of options on a reduced basis

Calibration of models is an important step in financial engineering. However it can be costly, especially in view of the increasing complexity of the models. s paper we explore the use of reduced basis as is done in fluid mechanics for the Navier–Stokes equations or as proposed by Maday, Patera and Turinici [Y. Maday et al., A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, J. Sci. Comput. 17 (1–4) (2002) 437–446]. It is shown that the method works well if we use convex combination of the basis functions instead of the more general linear combination; however, while this idea makes sense in view of the properties of the Black–Scholes equation, we have no proof to general linear combination; however, while this idea makes sense in view of the properties of the Black–Scholes equation, we have no proof to justify it mathematically. per presents a numerical investigation of the problem posed.