This paper continues the research started in [J. Štěpán and P. Dostál: The $\mathrm{d}X\left(t\right)=Xb\left(X\right)\mathrm{d}t+X\sigma \left(X\right)\mathrm{d}W$ equation and financial mathematics I. Kybernetika 39 (2003)]. Considering a stock price $X\left(t\right)$ born by the above semilinear SDE with $\sigma (x,t)=\tilde{\sigma }\left(x\left(t\right)\right),$ we suggest two methods how to compute the price of a general option $g\left(X\right(T\left)\right)$. The first, a more universal one, is based on a Monte Carlo procedure while the second one provides explicit formulas. We in this case need an information on the two dimensional distributions of $ℒ\left(Y\right(s),\tau (s\left)\right)$ for $s\ge 0,$ where $Y$ is the exponential...