The authors propose the following model for the log-price: \(R_\alpha(t)=D_t^\alpha X_t=\sigma_t D_t^\alpha B(\lambda(t))\), where \(D_t^\alpha\) is the Riemann-Liouville fractional derivative of order \(\alpha\), \(B\) is the classical Brownian motion, and \(\sigma_t\), \(\lambda\) are some nonrandom functions. A wavelet-based orthogonal expansion is derived for \(R_\alpha(t)\). The authors discuss finite-dimensional approximation, extrapolation and filtering problems for \(R_\alpha(t)\). Results of simulations are presented.