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- W2734444152 abstract "In financial mathematics, trading in an illiquid market has become a topic of great concern since assets in such market cannot be sold easily for cash without at least a minimal loss of value. This may be due to uncertainty traceable to factors like lack of interested buyers, transaction cost, and so on. Here, we obtain analytical solutions of a time-fractional nonlinear transaction-cost model for stock option valuation in an illiquid market through a relatively new semi-analytical method: modified differential transform method. Firstly, we considered a nonlinear option pricing model obtained when the constant volatility assumption of the classical linear Black–Scholes option pricing model is relaxed by including transaction cost. Thereafter, we extend, for the first time in literature, this nonlinear option pricing model to a time-fractional ordered form, and obtain approximate-analytical solutions to this new nonlinear model via the proposed technique. For efficiency and reliability of the method, two cases with five examples are considered: case 1 with two examples for time-integer order, and case 2 with three examples for time-fractional order. Our results strongly agree with the associated exact solutions in literature and those obtained via the application of Adomian Decomposition Method (ADM) even though our approximate solutions include only terms up to time power two, accuracy is improved for more terms. This therefore, shows that the result obtained via the ADM is a particular case of this present work when α = 1. Maple 18 software is used for the computations done in this work." @default.
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- W2734444152 date "2017-01-01" @default.
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- W2734444152 title "Analytical solutions of a time-fractional nonlinear transaction-cost model for stock option valuation in an illiquid market setting driven by a relaxed Black–Scholes assumption" @default.
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- W2734444152 doi "https://doi.org/10.1080/23311835.2017.1352118" @default.
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