The option valuation when the security model is a process of mixed type

The history of option valuation problem goes back to the year 1900 when Louis Bachelier deduced on option valuation formula under the assumption that the price process follows standard Brownian motion. More than 50 years later, the research for a mathematical theory of option valuation was taken up by Samuelson ([6]) and others. This work was brought into focus in the major paper by Black and Scholes ([1]) in which a complete option valuation model was derived on the assumption that the underlying price model is a geometric Brownian motion. THis paper starts with subjects developed mainly in Harrison and Kreps ([4]) and in Harrison and Pliska ([5]). The ideas established in these papers are essential for option valuation problem, and in particularfor the point of view that we take in this paper.