Coupled transform method for time-space fractional Black-Scholes option pricing model
S. O. Edeki, Rajarama Mohan Jena, Snehashish Chakraverty, Dumitru Bǎleanu
Abstract
This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended.
Topics & Concepts
Black–Scholes modelFractional calculusMathematicsApplied mathematicsExtension (predicate logic)Integer (computer science)Consistency (knowledge bases)Valuation of optionsDifferential (mechanical device)Space (punctuation)Mathematical optimizationComputer scienceEconometricsDiscrete mathematicsPhysicsProgramming languageThermodynamicsOperating systemVolatility (finance)Fractional Differential Equations SolutionsFinancial Risk and Volatility ModelingStatistical Distribution Estimation and Applications