Efficient simulation of prices for European call options under Heston stochastic-local volatility model: a comparison of methods

Abstract

The Heston stochastic-local volatility model, consisting of a asset price process and a Cox--Ingersoll--Ross-type variance process, offers a wide range of applications in the financial industry. The pursuit for efficient model evaluation has been assiduously ongoing and central to which is the numerical simulation of CIR process. Different from the weakly convergent noncentral chi-squared approximation used in 25, this paper considers two strongly convergent and positivity-preserving methods for CIR process under Lamperti transformation, namely, the truncated Euler method and the backward Euler method. It should be noted that these two methods are completely different. The explicit truncated Euler method is computationally effective and remains robust under high volatility, while the implicit backward Euler method provides high computational accuracy and stable performance. Numerical experiments on European call options are presented to show the superiority of different methods.