WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 14, 2019
Coupled Transform for Approximate-Analytical Solutions of a Time-Fractional One-Factor Markovian Bond Pricing Model
Authors: ,
Abstract: In the theory of option pricing as regards financial mathematics, one-factor model represents a view that there exists one Wiener process in the definition of the short rate process indicating one source of randomness. In this paper, approximate-analytical solution of a time-fractional one-factor Markovian model for bond pricing is considered using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of modified differential transform method. The derivatives are defined in terms of Jumarie’s sense. Illustrations are considered with a view to clarifying the effectiveness of the proposed solution method, and the solutions are presented graphically based on some financial parameters at different values of the time-fractional order. It is noted that the method requires little knowledge of fractional calculus while obtaining the approximate-analytical solutions of fractional equations without neglecting or compromising the associated accuracy. In terms of extension, the approach can be extended to multi-factor models formulated in terms of stochastic dynamics.
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Keywords: Option pricing, Black Scholes model, RDTM, Fractional derivative, Analytical solutions, Markov process
Pages: 202-208
WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 14, 2019, Art. #25