Affiliations: Department of Mathematical and Statistical Sciences, University of Alberta, AB, Canada. E-mail: melnikov@ualberta.ca | Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine. E-mail: myus@univ.kiev.ua
Note: [] Address for correspondence: Alexander Melnikov, Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, Canada, T6G 2G1. E-mail: melnikov@ualberta.ca
Abstract: We consider a multidimensional financial market with stochastic interest rates. The market has a long-range dependent component which is modeled with the help of several fractional Brownian motions with the Hurst indices belonging to (3/4,1). Interval choice is motivated by both the mathematical and financial reasons. We develop the results of Hitsuda and Cheridito concerning semimartingale properties of the market containing a long-range dependent component with the high-valued Hurst index. We show how to reduce the market model with long-range dependence to semimartingale market and then apply the results of Amin and Jarrow concerning the markets with stochastic interest rates in order to prove the arbitrage-free property as well as to provide option pricing.
