Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

Foad Shokrollahi (), Adem Kılıçman and Marcin Magdziarz
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Foad Shokrollahi: Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
Adem Kılıçman: Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
Marcin Magdziarz: #x2020;Hugo Steinhaus Center, Department of Mathematics, Wrocław University of Technology, Wyspiańskiego 27, 50–370 Wrocław, Poland

International Journal of Financial Engineering (IJFE), 2016, vol. 03, issue 01, 1-22

Abstract: This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion (MFBM) model. The pricing method is obtained for European call option using the time-changed MFBM model in a discrete time setting. Particularly, the minimal value Cmin(t,St) of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed MFBM model. In addition, the impact of time step Δt, Hurst parameter H and transaction costs α are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed MFBM is a satisfactory model.

Keywords: Black–Scholes model; mixed fractional Brownian motion; inverse β-stable subordinator; subdiffusion (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1142/S2424786316500031

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