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# High order approximations of the Cox-Ingersoll-Ross process semigroup using random grids

1 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : 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) 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) for the CIR leads to weak approximations of order $2k$, for all $k\in\mathbb{N}^*$. 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.
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Type de document :
Pré-publication, Document de travail
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https://hal-enpc.archives-ouvertes.fr/hal-03791594
Contributeur : Aurélien Alfonsi Connectez-vous pour contacter le contributeur
Soumis le : jeudi 29 septembre 2022 - 12:53:26
Dernière modification le : mardi 25 octobre 2022 - 16:22:45

### Identifiants

• HAL Id : hal-03791594, version 1
• ARXIV : 2209.13334

### Citation

Aurélien Alfonsi, Edoardo Lombardo. High order approximations of the Cox-Ingersoll-Ross process semigroup using random grids. {date}. ⟨hal-03791594⟩

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