High order approximations of the Cox–Ingersoll–Ross process semigroup using random grids
July 1, 2024·
Edoardo Lombardo
Equal contribution
,Aurélien Alfonsi
Equal contribution
·
0 min readAbstract
We present new high order approximations schemes for the Cox–Ingersoll–Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021, Numer. Math.) for the approximation of semigroups. The idea consists in using a suitable combination of discretization schemes calculated on different random grids to increase the order of convergence. This technique coupled with the second order scheme proposed by Alfonsi (2010, Math. Comp.) for the CIR leads to weak approximations of all orders. Despite the singularity of the square-root volatility coefficient, we show rigorously this order of convergence under some restrictions on the volatility parameters. We illustrate numerically the convergence of these approximations for the CIR process and for the Heston stochastic volatility model and show the computational time gain they give.
Type
Publication
IMA Journal of Numerical Analysis
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.