Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models

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 price, 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.Comment: 34 pages, 5 figure

Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process

We study convergence properties of the full truncation Euler scheme for the Cox-Ingersoll-Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the Feller ratio is greater than three), we establish the strong order 1/2 convergence in $L^{p}$ of the scheme to the exact solution. This is consistent with the optimal rate of strong convergence for Euler approximations of stochastic differential equations with globally Lipschitz coefficients, despite the fact that the diffusion coefficient in the Cox-Ingersoll-Ross model is not Lipschitz.Comment: 16 pages, 1 figur

Parasitic fauna in farmed trouts in Tismana, Romania

Epidemiological study of the general prevalence of parasites in trouts in the two farms from have revealed various aspects depending on the species studied, depending on season, age category (size) but also from a farm to another