cZ(t) for all s,t 0 and c > 0. According to the defini-

The study and the analysis on the empirical behavior of data (see, among others, Akigiray (1989) Campbell (1987), Fama and French (1988) French, Schwert and Stambaugh (1987)) have reported evidence that conditional first and second moments of stock returns are time varying and potentially persistent especially when returns are measured over long horizons. For a general approach to contingent claim pricing based on a diffusion model for asset returns with stochastic and path dependent volatilities we could refer to Hofmann, Platen and Schweizer (1982), Duan (1995), Kalsen and Taqqu (1998).