An accurate heston implementation with Usd-Cop Data

Abstract

This study find by empirical evidence a fast and accurate way to calculate the price of a European Call using the Heston (1993) model. It calculate and uses a benchmark price calculated with the mentioned Heston 1993 pricing approaches and the trapezoidal rule with a = 1e-20000; b = 300; N = 10000000, to find which combination of Heston pricing process and numerical schems leads to a computationally faster and more accurate price process. Two equivalent pricing methods and seven numerical schemes are calculated in order to find wich combination take less time to be compute and is closes to the benchmark as posible. The study uses Q-measure in the sense of spot data, and the other P-measure in the sense of historical data. That mean the study calculate two parameter sets. one under mesure Q and other under P by Maximum Likelihood and non-linear least square function, respectively, to somehow proof the conclution dose not depents on how the parameter are found. Study stands that the accuraste way to calculate the Heston price in the Colombian FX market data used is consolidating the integrals for the probability P1 and P2 that the original framework propose and solve the integral using Gauss-Legendre or Gauss-Laguerre.