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Pricing option with stochastic interest rates and transaction costs in fractional Brownian markets. (English) Zbl 1422.91722

Summary: This work deals with European option pricing problem in fractional Brownian markets. Two factors, stochastic interest rates and transaction costs, are taken into account. By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession. Pricing formulas are derived by the variable substitution and the classical solution of the heat conduction equation. By the mathematical software and the parameter estimation methods, the results are reported and compared with the data from the financial market.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60G22 Fractional processes, including fractional Brownian motion
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