Estimation of Stochastic Trend on Ukrainian Stock Market

The paper presents a new approach for price dynamic assessment on the Ukrainian stock market based on a qualitative modification of the Black-Scholes-Merton model for estimating unknown parameters with a stochastic trend. The mean-reverting Ornstein-Uhlenbeck process was chosen as the time-dependent trend parameter since it is both mathematically convenient and has a natural economic interpretation. In order to estimate the parameters of the corresponding stochastic diffusion, the trajectory-fitting technique based on the Kalman-Bucy filter was used. The proposed approach was then tested on UX-index assets.