Meshless approach for pricing Islamic Ijarah under stochastic inter- est rate models

Nowadays, the fixed interest rate nancing method is commonly used in the capitalist nancial system and in a wide range of nancial liability instruments, the most important of which is bond. In the Islamic nancial system, using these instruments is considered as usury and has been prohibited. In fact, Islamic law, Shariah, forbids Muslims from receiving or paying the Riba. Therefore, using customary nancial instruments such as bond is not acceptable or applicable in countries which have a majority of Muslim citizens. In this paper, we introduce one nancial 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 xed 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