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[en] Highlights: • An efficient MC method for the sensitivity calculation of reactivity coefficients is developed. • The sensitivity of reactivity coefficient is calculated by MC second-order perturbation techniques. • Its effectiveness is examined in a two-group homogeneous problem and Godiva. • S/U analyses are performed for MDC of a LWR pin cell and FTC of a CANDU 6 lattice model. - Abstract: The uncertainty quantification of the reactivity coefficients such as the fuel temperature coefficient (FTC) and the moderator density coefficient (MDC) is crucial for the nuclear reactor safety margin evaluation. This paper proposes a continuous-energy MC second-order perturbation (MC2P) method as a new way to estimate efficiently the sensitivity of reactivity coefficients to nuclear cross section data. The proposed MC2P method takes into account the second-order effects of the fission operator and the fission source distribution. The effectiveness of the MC2P method implemented in a Seoul National University MC code, McCARD, is demonstrated in a Godiva 235U density coefficient problem via comparison of its results with direct subtraction MC calculation. It is shown that the new method can predict the cross section sensitivities of the reactivity coefficient more accurately even with much smaller number of MC history simulations than the direct subtraction MC method. It is also shown that the proposed method is applicable for quantifying the uncertainties of the MDC of a LWR pin cell problem and the FTC of a CANDU 6 lattice cell problem due to the uncertainties of the nuclear cross section input data represented by nuclear cross section covariance data.