High Order Approximations and Simulation Schemes for the Log-Heston Process
January 1, 2025·
Edoardo Lombardo
Equal contribution
,Aurélien Alfonsi
Equal contribution
·
0 min readAbstract
We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random grids to increase the order of convergence. We apply this method with either the Ninomiya–Victoir scheme (2008) or a second order scheme that samples exactly the volatility component, and we show rigorously that we can achieve then any order of convergence. We give numerical illustrations on financial examples that validate the theoretical order of convergence. We also present promising numerical results for the multifactor/rough Heston model and hint at applications to other models, including the Bates model and the double Heston model.
Type
Publication
Siam Journal on Financial Mathematics
Authors
Quantitative Researcher, Ph.D.
I am a Quantitative Researcher and Applied Mathematician with a Ph.D. from École des Ponts ParisTech and University of Roma Tor Vergata. My expertise lies at the intersection of stochastic calculus, high-performance computing, and numerical methods. I specialize in modeling complex stochastic dynamics and building high-performance numerical solutions in C++ and Python, transforming advanced mathematical theory into fast, accurate pricing and risk infrastructure. With prior industry experience as a Quantitative Analyst at Enel and Risk Analyst at AXA, I am passionate about applying advanced mathematical techniques, Monte Carlo simulations, and data-driven methods to solve complex pricing, risk, and alpha-generation problems in financial markets.