Weak Error Rates for Numerical Schemes of Nonsingular Stochastic Volterra Equations with Application to Stochastic Volatility Models

Bras, Pierre; Fukasawa, Masaaki

SIAM Journal on Financial Mathematics, 2025, 16(1), 1-28

アクセス数:30件（2025-08-15 23:28 集計）

固定URL: https://hdl.handle.net/11094/101995

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論文情報

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タイトル
Weak Error Rates for Numerical Schemes of Nonsingular Stochastic Volterra Equations with Application to Stochastic Volatility Models
著者
著者名
Bras, Pierre
NRID
1000070506451 1000070506451
ORCID
0000-0002-0848-5001 0000-0002-0848-5001
researchmap permalink
read0140655 read0140655
Scopus Author ID
24366273400 24366273400
著者名
Fukasawa, Masaaki
キーワード等
stochastic Volterra equation
rough volatility
Euler-Maruyama scheme
weak error rate
内容
Bras P., Fukasawa M.. Weak Error Rates for Numerical Schemes of Nonsingular Stochastic Volterra Equations with Application to Stochastic Volatility Models. SIAM Journal on Financial Mathematics 16, 1 (2025); https://doi.org/10.1137/23M155671X.
抄録
We study the weak error rate for the Euler-Maruyama scheme for stochastic Volterra equations (SVEs) with application to pricing under stochastic volatility models. SVEs are non-Markovian stochastic differential equations with memory kernel. We assume in particular that the kernel is nonsingular and C⁴. We show that the weak error rate is of order O(1/N) where N is the number of steps of the Euler-Maruyama scheme, thus giving the same weak error rate as for SDEs. Our proof consists in adapting the classic weak error proof for Markov processes to SVEs; to this end we rely on infinite dimensional functionals and on their derivatives.
出版者
Society for Industrial and Applied Mathematics Publications
収録物名
SIAM Journal on Financial Mathematics
巻(号)
16(1)
ページ
1-28
刊行年月
2025-01-08
言語
英語
ハンドルURL
https://hdl.handle.net/11094/101995
eISSN
1945497X
関連情報 (isVersionOf)
DOI (出版社版)
https://doi.org/10.1137/23M155671X
アクセス権
open access
権利情報
© 2025 Society for Industrial and Applied Mathematics.
出版タイプ
Accepted Manuscript
カテゴリ
学術雑誌論文 Journal Article