  We model the price of a stock via a Lang\'{e}vin equation with
multi-dimensional fluctuations coupled in the price and in time. We generalize
previous models in that we assume that the fluctuations conditioned on the time
step are compound Poisson processes with operator stable jump intensities. We
derive exact relations for Fourier transforms of the jump intensity in case of
different scaling indices $\underline{\underline{E}}$ of the process. We
express the Fourier transform of the joint probability density of the process
to attain given values at several different times and to attain a given maximal
value in a given time period through Fourier transforms of the jump intensity.
Then we consider a portfolio composed of stocks and of options on stocks and we
derive the Fourier transform of a random variable $\mathfrak{D}_t$ (deviation
of the portfolio) that is defined as a small temporal change of the portfolio
diminished by the the compound interest earned. We show that if the price of
the option at time $t$ satisfies a certain functional equation specified in
text then the deviation of the portfolio has a zero mean $E[ \mathfrak{D}_t ] =
0$ and the option pricing problem may have a solution. We compare our approach
to other approaches that assumed the log-characteristic function of the
fluctuations that drive the stock price to be an analytic function.
