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.
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