Parametric Monte Carlo with Chebyshev Interpolation

We propose to reduce the computational complexity of the evaluation of parametric expectations by (tensorized Chebyshev interpolation). Fast and acchurate evaluation of parametric expectations is a frequently occuring task in finance. Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. 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 combined with Monte-Carlo for multivariate and path-dependent options. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte-Carlo.