Summary: We consider Ornstein-Uhlenbeck process \(x_t=x_0 e^{-\theta t} + \mu(1-e^{-\theta t})+\sigma \int\limits_0^t e^{-\theta(t-s)} dW_s\), where \(x_0\in \mathbb{R}\), \(\theta > 0\), \(\mu \in \mathbb{R}\), \(\sigma > 0\) and \(W_s\) are Wiener process. By using the values \((z_k)_{k\in N}\) of the corresponding trajectories at a fixed positive moment \(t\), the estimates \(T_n\) and \(T_n^{\ast \ast}\) of unknown parameters \(x_0\) and \(\theta\) are constructed, where \(x_0\) is an underlying asset initial price and \(\theta\) is a rate by which these shocks dissipate and the variable reverts towards the mean in the Ornstein-Uhlenbeck’s stochastic process. By using Kolmogorov’s Strong Law of Large Numbers the consistence of estimates \(T_n\) and \(T_n^{\ast \ast}\).