Chebyshev Interpolation for Parametric Option Pricing

Abstract

Function approximation with Chebyshev polynomials is a well-established and thoroughly investigated method within the field of numerical analysis. The method enjoys attractive convergence properties and its implementation is straightforward. We propose to apply tensorized Chebyshev interpolation to computing Parametric Option Prices (POP). This allows us to exploit the recurrent nature of the pricing problem in an efficient, reliable and general way. For a large variety of option types and affine asset models we prove that the convergence rate of the method is exponential if there is a single varying parameter and of any arbitrary polynomial order in the multivariate case. Numerical experiments confirm these findings and show that the method achieves a significant gain in efficiency.