Author
Cozma, A
Reisinger, C
Journal title
SIAM JOURNAL ON NUMERICAL ANALYSIS
DOI
10.1137/17M1136754
Issue
6
Last updated
2024-03-26T19:49:56.99+00:00
Abstract
© 2018 Society for Industrial and Applied Mathematics. We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot process, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler-Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state of the art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which is moreover consistent with that for Lipschitz coefficients and hence optimal.
Symplectic ID
919062
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Publication type
Journal Article
Publication date
01 Jan 2018
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