Chebyshev interpolation for multivariate real-time problems in finance

Real-time methods for option pricing and the computation of risk quantities in multivariate settings are required in order to pave the way for innovation in financial digitalization. The development of such methods poses a... [ view full abstract ]

Real-time methods for option pricing and the computation of risk quantities in multivariate settings are required in order to pave the way for innovation in financial digitalization. The development of such methods poses a serious challenge. Considering Parametric Option Pricing (POP) we show that polynomial interpolation in the parameter space considerably reduces run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence. Combined with Monte Carlo simulation and low rank tensor techniques the Chebyshev method turns out to yield very promising result for high dimensional problems.