Variational sensitivity analysis of parametric Markovian market models

• Autorzy: Norbert Hilber , Christoph Schwab , Christoph Winter
• Języki publikacji: EN

Abstrakty

EN

Parameter sensitivities of prices for derivative contracts play an important role in model calibration as well as in quantification of model risk. In this paper a unified approach to the efficient numerical computation of all sensitivities for Markovian market models is presented. Variational approximations of the integro-differential equations corresponding to the infinitesimal generators of the market model differentiated with respect to the model parameters are employed. Superconvergent approximations to second and higher derivatives of prices with respect to the price process' state variables are extracted from approximate, computed prices with low, C⁰ regularity by postprocessing. The extracted numerical sensitivities are proved to converge with optimal rates as the mesh width tends to zero. Numerical experiments for uni- and multivariate models with sparse tensor product discretization confirm the theoretical results.

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 60J25: Continuous-time Markov processes on general state spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 83
• Numer: 1
• Strony: 85-106

Daty

wydano

2008

Twórcy

autor

Norbert Hilber

• Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

autor

Christoph Schwab

• Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

autor

Christoph Winter

• Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

Identyfikatory

DOI

10.4064/bc83-0-6