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## A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series

#### Mehmet Yavuz [1] , Necati Özdemir [2]

##### 78 255

This study addresses a novel identification of Adomian Decomposition Method (ADM) to have an accurate and quick solution for the European option pricing problem by using Black-Scholes equation of time-fractional order (FBSE) with the initial condition and generalized Black-Scholes equation of fractional order (GFBSE). The fractional operator is understood in the Caputo mean. First of all, we redefine the Black-Scholes equation as fractional mean which computes the option price for fractional values. Then we have applied the ADM to the FBSE and GFBSE, so we have obtained accurate and quick approximate analytical solutions for these equations. The results related to the solutions have been presented in figures.

Adomian decomposition method, convergence analysis, fractional Black-Scholes model, option pricing
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Primary Language en Engineering Articles Orcid: orcid.org/0000-0002-3966-6518Author: Mehmet Yavuz (Primary Author)Institution: Necmettin Erbakan UniversityCountry: Turkey Author: Necati ÖzdemirInstitution: Balikesir UniversityCountry: Turkey Publication Date: April 15, 2018
 Bibtex @research article { konuralpjournalmath359520, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2018}, volume = {6}, pages = {102 - 109}, doi = {}, title = {A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series}, key = {cite}, author = {Yavuz, Mehmet and Özdemir, Necati} } APA Yavuz, M , Özdemir, N . (2018). A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series. Konuralp Journal of Mathematics (KJM), 6 (1), 102-109. Retrieved from http://dergipark.org.tr/konuralpjournalmath/issue/31478/359520 MLA Yavuz, M , Özdemir, N . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 (2018): 102-109 Chicago Yavuz, M , Özdemir, N . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 (2018): 102-109 RIS TY - JOUR T1 - A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series AU - Mehmet Yavuz , Necati Özdemir Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 102 EP - 109 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics (KJM) A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series %A Mehmet Yavuz , Necati Özdemir %T A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series %D 2018 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 6 %N 1 %R %U ISNAD Yavuz, Mehmet , Özdemir, Necati . "A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series". Konuralp Journal of Mathematics (KJM) 6 / 1 (April 2018): 102-109. AMA Yavuz M , Özdemir N . A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series. Konuralp J. Math.. 2018; 6(1): 102-109. Vancouver Yavuz M , Özdemir N . A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series. Konuralp Journal of Mathematics (KJM). 2018; 6(1): 109-102.