Unlike Riemann integral, the definition of various stochastic integrals, in which the infinitesimal is $dB_t$, where $\{B_t\}_{t\ge0}$ is a Brownian motion process, depends on the position of the sample points within the subintervals of a partition. Thus when the sample points are chosen at the beginning of the subintervals, we obtain the Itô integral, while when the sample points are the midpoints, we get the Stratonovich integral. We may choose the sample points such that they divide the subintervals of a partition in a certain ratio $\lambda$, and obtain a specific stochastic integral. It turns out that the ratio $\lambda$ corresponds to a certain generalized Wick product. We present sharp inequalities about the $L^p$ norms of the generalized Wick product of two random variables. In order to make the generalized Wick product bounded, we need to employ also the second quantization operators. As a limiting case of our Wick product inequalities, we derive Nelson hypercontractivity inequality.