Fast numerical simulation of a new time-space fractional option pricing model governing European call option
V. Anh and
Applied Mathematics and Computation, 2018, vol. 339, issue C, 186-198
When the fluctuation of option price is regarded as a fractal transmission system and the stock price follows a Lévy distribution, a time-space fractional option pricing model (TSFOPM) is obtained. Then we discuss the numerical simulation of the TSFOPM. A discrete implicit numerical scheme with a second-order accuracy in space and a 2−γ order accuracy in time is constructed, where γ is a transmission exponent. The stability and convergence of the obtained numerical scheme are analyzed. Moreover, a fast bi-conjugate gradient stabilized method is proposed to solve the numerical scheme in order to reduce the storage space and computational cost. Then a numerical example with exact solution is presented to demonstrate the accuracy and effectiveness of the proposed numerical method. Finally, the TSFOPM and the above numerical technique are applied to price European call option. The characteristics of the fractional option pricing model are analyzed in comparison with the classical Black–Scholes (B-S) model.
Keywords: Time-space fractional option pricing model; Modified Riemann–Liouville fractional derivative; Caputo fractional derivative; European call option; Fast numerical simulation (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:186-198
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().