Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process

Xiaohan Li; Wei Liu; Xuerong Mao; Yue Wu

doi:10.48550/arXiv.2502.00788

Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process

Xiaohan Li, Wei Liu^*, Xuerong Mao, Yue Wu

^*Corresponding author for this work

Mathematics And Statistics

Research output: Working paper/Preprint/Pre-registration › Working Paper/Preprint

Abstract

In this paper, we introduce a linear stochastic volatility model driven by α-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of 1/α. Numerical simulations are presented at the end to verify theoretical results.

Original language	English
Place of Publication	Ithaca, NY
Pages	1-25
Number of pages	25
DOIs	https://doi.org/10.48550/arXiv.2502.00788
Publication status	Published - 2 Feb 2025

Keywords

stochastic volatility models
α-stable process
positivity preserving Euler-Maruyama scheme
strong convergence
numerical simulation

Access to Document

10.48550/arXiv.2502.00788

Cite this

@techreport{6a6133a5bc4a42d39144f562ba3f3e77,

title = "Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process",

abstract = "In this paper, we introduce a linear stochastic volatility model driven by α-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of 1/α. Numerical simulations are presented at the end to verify theoretical results.",

keywords = "stochastic volatility models, α-stable process, positivity preserving Euler-Maruyama scheme, strong convergence, numerical simulation",

author = "Xiaohan Li and Wei Liu and Xuerong Mao and Yue Wu",

year = "2025",

month = feb,

day = "2",

doi = "10.48550/arXiv.2502.00788",

language = "English",

pages = "1--25",

type = "WorkingPaper",

}

TY - UNPB

T1 - Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process

AU - Li, Xiaohan

AU - Liu, Wei

AU - Mao, Xuerong

AU - Wu, Yue

PY - 2025/2/2

Y1 - 2025/2/2

N2 - In this paper, we introduce a linear stochastic volatility model driven by α-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of 1/α. Numerical simulations are presented at the end to verify theoretical results.

AB - In this paper, we introduce a linear stochastic volatility model driven by α-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of 1/α. Numerical simulations are presented at the end to verify theoretical results.

KW - stochastic volatility models

KW - α-stable process

KW - positivity preserving Euler-Maruyama scheme

KW - strong convergence

KW - numerical simulation

U2 - 10.48550/arXiv.2502.00788

DO - 10.48550/arXiv.2502.00788

M3 - Working Paper/Preprint

SP - 1

EP - 25

BT - Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process

CY - Ithaca, NY

ER -

Explicit positivity preserving numerical method for linear stochastic volatility models driven by α-stable process

Abstract

Keywords

Access to Document

Fingerprint

Cite this