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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

Edeki, S.O. and Ugbebor, O. O. and Owoloko, E. A. (2017) 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. Cogent Mathematics , 4. pp. 1-14.

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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 timefractional order. Our results strongly agree with the associated exact solutions in

Item Type: Article
Uncontrolled Keywords: fractional calculus; nonlinear Black–Scholes model; illiquid market; option pricing; MDTM
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Mrs Aderonke Olufunke Asaolu
Date Deposited: 28 Aug 2017 17:18
Last Modified: 28 Aug 2017 17:18
URI: http://eprints.covenantuniversity.edu.ng/id/eprint/8954

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