STOCHASTIC FINANCIAL MODEL BASED ON FRACTIONAL BROWN MOTION

Abstract

Fractional brown motion (FBM) is featured by long-term memory and selfsimilarity compared to standard brown motion.  Because of the properties, it can be used to describe the phenomenon (e.g. seasonal effect, scale effect and sharp peak and heavy tail) which cannot be described by some typical analytical methods in financial market.  The fractal features of fractional brown motion make it a more suitable tool in financial studies.  This study simulated the increment of FBM and the square of the increment using extended Maruyama symbols as well as the change path of underlying asset price and obtained the formula for European option pricing using insurance actuary pricing.