  Recurrent tasks such as pricing, calibration and risk assessment need to be
executed accurately and in real-time. Simultaneously we observe an increase in
model sophistication on the one hand and growing demands on the quality of risk
management on the other. To address the resulting computational challenges, it
is natural to exploit the recurrent nature of these tasks. We concentrate on
Parametric Option Pricing (POP) and show that polynomial interpolation in the
parameter space promises to reduce run-times while maintaining accuracy. The
attractive properties of Chebyshev interpolation and its tensorized extension
enable us to identify criteria for (sub)exponential convergence and explicit
error bounds. We show that these results apply to a variety of European
(basket) options and affine asset models. Numerical experiments confirm our
findings. Exploring the potential of the method further, we empirically
investigate the efficiency of the Chebyshev method for multivariate and
path-dependent options.
