2015/05/18 by Maximilian Gaß, Gaß, Maximilian, Kathrin Glau +5 · 1 citation
Economics, Econometrics and Finance · Engineering · #41A10 #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1505.04648
openalex publication_date 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.