Variational sensitivity analysis of parametric Markovian market models

Norbert Hilber, Christoph Schwab, and Christoph Winter. "Variational sensitivity analysis of parametric Markovian market models." Banach Center Publications 83.1 (2008): 85-106. <http://eudml.org/doc/282092>.

@article{NorbertHilber2008,
abstract = {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.},
author = {Norbert Hilber, Christoph Schwab, Christoph Winter},
journal = {Banach Center Publications},
keywords = {Markov process; Greeks; sensitivity; sparse tensor finite elements},
language = {eng},
number = {1},
pages = {85-106},
title = {Variational sensitivity analysis of parametric Markovian market models},
url = {http://eudml.org/doc/282092},
volume = {83},
year = {2008},
}

TY - JOUR
AU - Norbert Hilber
AU - Christoph Schwab
AU - Christoph Winter
TI - Variational sensitivity analysis of parametric Markovian market models
JO - Banach Center Publications
PY - 2008
VL - 83
IS - 1
SP - 85
EP - 106
AB - 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.
LA - eng
KW - Markov process; Greeks; sensitivity; sparse tensor finite elements
UR - http://eudml.org/doc/282092
ER -