Meshless approach for pricing Islamic Ijarah under stochastic interest rate models

Document Type : Research Paper


Department of Mathematics, Statistics and Computer, Allameh Tabataba’i University, Tehran, Iran.


Nowadays, the fixed interest rate financing method is commonly used in the capitalist financial system and in a wide range of financial liability instruments, the most important of which is bond. In the Islamic financial system, using these instruments is considered as usury and has been prohibited. In fact, Islamic law, Shariah, forbids Muslims from receiving or paying off the Riba. Therefore, using customary financial instruments such as bond is not acceptable or applicable in countries which have a majority of Muslim citizens. In this paper, we introduce one financial instrument, Sukuk, as a securities-based asset under stochastic income. These securities can be traded in secondary markets based on the Shariah law. To this end, this paper will focus on the most common structure of the Islamic bond, the Ijarah and its negotiation mechanism. Then, by presenting the short-term stochastic model, we solve fixed interest rate and model the securities-based asset by the stochastic model. Finally, we approximate the resulting model by radial basis function method, as well as utilizing the Matlab software.


  • [1]          B. Acciaio, C. Fontana, and C. Kardaras, Arbitrage of the first kind and filtra- tion enlargements in semimartingale financial models, Stoch. Proc. Appl., 126(6) (2018), 1761–1784.
  • [2]          S. Al-Suwailem, Towards an objective measure of gharar in exchange, Islamic Economic Studies, 7(1) (2000), 61–102.
  • [3]          S. P. Azizi and A. Neisy, A New Approach in Geometric Brownian Motion Model. In: Cao BY. (eds) Fuzzy Information and Engineering and Decision. IWDS 2016. Advances in Intelligent Systems and Computing, 646 (2018), 336–342.
  • [4]          S. Cuomo, V. Di Somma, and F. Sica, A note on the numerical resolution of  Heston PDEs, Ric. Mat., (2020), 1–8.
  • [5]          S. Cuomo, F. Sica, and G. Toraldo, Greeks computation in the option pricing problem by means of RBF-PU methods, J. Comput. Appl. Math., 376 (2020), 112882.
  • [6]          S. De Marchi, A. Martinez, E. Perracchione, and M. Rossini, RBF-based partition of unity methods for elliptic PDEs: Adaptivity and  stability  issue  via  variable  scaled kernels, J. Sci. Comput., 79(2) (2019), 321–324.
  • [7]          M. A. El-Gamal, A basic guide to  contemporary  Islamic  banking  and  finance,  Rice University Houston, 1 (2000).
  • [8]          M. A. Elgari., Short term financial instruments based on salam contracts, In Ahmed & T. Khan (Eds.), Islamic financial instruments for public sector resource mobilization, Jeddah: Islamic Research and Training Institute, Islamic Development Bank, (1997), 249–266.
  • [9]          C. Fontana, Z. Grbac, S. Gumbel, and T. Schmidt, Term structure modeling for multiple curves with stochastic discontinuities, Financ. Stoch., (2020), 1–47.
  • [10]        N. Ul Haque and A. Mirakhor, The design of instruments for government finance in an Islamic economy, University Library of Munich, 56028 (1999).
  • [11]        M. Kahf, The use of assets Ijara bonds for bridging the budget gap, Islamic Eco- nomic Studies, 4(2) (1997), 75–92.
  • [12]        Y-K, Kwok.,Mathematical Models of Financial Derivatives, Springer Publication, (2008).
  • [13]        E. Larsson, K. Ahlander, and A. Hall. Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform, J. Comput. Appl. Math., 22(1) (2008), 175–192.
  • [14]        E. Larsson and B. Fornberg, A numerical study of some Radial Basis Func-  tion Based Solution Methods for Eliptic PDEs, Comput. Math. with Appl, 46(5) (2003), 891–902.
  • [15]        R. Mohammadinejad, J. Biazar, and A. Neisy, Spread option pricing using two jump-diffusion interest rates, Univ. Politehnica Bucharest, Sci Bull., 82(1) (2020), 171–182.
  • [16]        U. Pettersson, E. Larsson, G. Marcusson, and J. Persson, Improved radial basis function methods for multi-dimensional option pricing, J. Comput. Appl. Math., 222 (2008), 82–93.
  • [17]        M. Safaei, A. Neisym, and N. Nematollahi, New splitting scheme for pricing American options under the Heston model, Comput. Econ., 52(2) (2013), 405– 420.
  • [18]        M. A. Shahrokhabadi, A. Neisy, E. Perracchione, and M. polato, Learning with re- duced kernel-based methods: Environmental and financial applications, Dolomites Research Notes on Approximation-Padova university Press., 12 (2019), 12–27.
  • [19]        A. Zarka, Istisna’financing of infrastructure projects, Islamic Economic Studies,
  • 4(2) (2000), 67-74.