The Convergence Investigation of a Numerical Scheme for the Tempered Fractional Black-Scholes Model Arising European Double Barrier Option

Author(s):  
Y. Esmaeelzade Aghdam ◽  
H. Mesgarani ◽  
A. Adl ◽  
B. Farnam
Author(s):  
Amirhossein Sobhani ◽  
mariyan milev

In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. With regard to the well-known Black-Scholes model, the price of an option in each monitoring date could be calculated by computing a recursive integral formula that is based on the heat equation solution. We have approximated these recursive solutions with the aid of Lagrange interpolation on Jacobi polynomial nodes. After that, an operational matrix, that makes our computation significantly fast, has been derived. In some theorems, the convergence of the presented method has been shown and the rate of convergence has been derived. The most important benefit of this method is that its complexity is very low and does not depend on the number of monitoring dates. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.


2021 ◽  
Vol 6 (6) ◽  
pp. 5750-5761
Author(s):  
Kazem Nouri ◽  
◽  
Milad Fahimi ◽  
Leila Torkzadeh ◽  
Dumitru Baleanu ◽  
...  

2020 ◽  
Vol 14 (1) ◽  
pp. 91-96
Author(s):  
Fatemeh Kamalzadeh ◽  
Rahman Farnoosh ◽  
Kianoosh Fathi

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Juan He ◽  
Aiqing Zhang

We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system. In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM. The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction. Energy analysis indicates that the constructed discrete method is unconditionally stable. Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively. Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme. At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.


2013 ◽  
Vol 16 (08) ◽  
pp. 1350044 ◽  
Author(s):  
SÜHAN ALTAY ◽  
STEFAN GERHOLD ◽  
RAINER HAIDINGER ◽  
KARIN HIRHAGER

We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black–Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose individual coupons are digital double barrier options. This value can also be approximated by the price of a corridor put.


2021 ◽  
Vol 1734 ◽  
pp. 012055
Author(s):  
S. O. Edeki ◽  
R. M. Jena ◽  
O. P. Ogundile ◽  
S. Chakraverty

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