Calibration of options on a reduced basis

  • Authors:

  • Olivier Pironneau

  • Affiliations:

  • Laboratoire Jacques-Louis Lions, Université Paris VI, I.U.F., France

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

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. In this 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. The paper presents a numerical investigation of the problem posed.