European option pricing by using a mixed fractional Brownian motion

Financial modeling is conventionally based on a Brownian motion (Bm). A Bm is a semimartingale process with independent and stationary increments. However, some financial data do not support this assumption. One of the models that can overcome this problem is a fractional Brownian motion (fBm). In fact, the main problem in option pricing by implementing an fBm is not arbitrage-free. This problem can be handled by using a mixed fBm (mfBm) to model stock prices. The mfBm is a linear combination of an fBm and an independent Bm. The aim of this paper is to find European option pricing by using the mfBm based on Fourier transform method and quasi-conditional expectations. The main result of this research is a closed form formula for calculating the price of European call options.