On the convergence of He and Zhu's new series solution for pricing options with the Heston model

In this paper, a modified formula for European options and a set of complete convergence proofs for the solution that cover the entire time horizon of a European option contact are presented under the Heston model with minimal entropy martingale measure. Although He & Zhu [5] worked on this model, they only provided a converged solution with a condition imposed on the time to expiry. The new solution presented here is only slightly modified in its form. But, it is accompanied with the proof of convergence of the solution for the entire span of the time horizon of an option.