  This article present a continuous cascade model of volatility formulated as a
stochastic differential equation. Two independent Brownian motions are
introduced as random sources triggering the volatility cascade. One
multiplicatively combines with volatility; the other does so additively.
Assuming that the latter acts perturbatively on the system, then the model
parameters are estimated by application to an actual stock price time series.
Numerical calculation of the Fokker--Planck equation derived from the
stochastic differential equation is conducted using the estimated values of
parameters. The results reproduce the pdf of the empirical volatility, the
multifractality of the time series, and other empirical facts.
