Option pricing by using a mixed fractional Brownian motion with jumps. (February 2019)

• Record Type: Journal Article
• Authors: Murwaningtyas, Chatarina Enny; Kartiko, Sri Haryatmi; Gunardi, ; Suryawan, Herry Pribawanto
• Is Part Of: Journal of physics. Volume 1180(2019)
• Publication Date: 2019-02
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1180/1/012011
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: Option pricing is conventionally based on a Brownian motion (Bm). The Bm is a semimartingale process with stationary and independent increments. However, there are several stock returns that have a long memory or have high autocorrelation for long lags. A fractional Brownian motion (fBm) is one of the models that can solve this problem, but a model option with fBm is not arbitrage-free. A mixed fractional Brownian motion (mfBm) is a linear combination of a Bm and an independent fBm which can overcome the arbitrage problem. A jump process in time series is another problem found in stock price modeling. This paper deals with the problem of options pricing by using mfBm with jumps. Based on quasi-conditional expectation and Fourier transform method, we obtain a pricing formula for a stock option.