Commodity salam contracts models as shariah compliance financial derivatives / Azie Farhani Badrol Hisham - Badrol Hisham, Azie Farhani (2021)
There are several Islamic contracts which can be developed as shariah compliance derivatives, namely salam, urbun and istijrar. However, this study focuses on commodity salam contract since there are a lot of discussions concerning permissibility, criteria and conditions of salam contract in the literature. From the definition, the salam contract is closely resembling prepaid forward contract. However, there are some criteria and conditions that make it different from the conventional prepaid forward such as the predetermined salam price that has the discount element to compensate the buyer from credit default risk, the stochastic behavior of the underlying asset and the unique terminal boundary condition of salam contract. Although many studies and discussions had been done on salam contract, they are more on qualitative studies. Hence, this study aims to develop the mathematical models of commodity salam contracts in pricing the salam price. In developing the shariah compliance models of commodity salam, this study has identified the appropriate variables to represent the principals and price criteria of the salam contracts. Then, unique boundary conditions and profit equations of both salam contracts have been proposed. For the case of salam contract between two parties, this study has adopted the concept of Islamic time value of money to price the commodity salam. Four mathematical models of commodity salam contract between two parties in discrete and continuous time series have been successfully developed which are CS_2PSD Model, CS_2PCD Model, CS_2PPCD Model and CS_2PCC Model. Apart from that, three mathematical methods have been used to model the traded commodity salam contract as an actively traded shariah compliance derivative by utilizing the Brownian motion theory. The first one is by adopting the basic foundation of no arbitrage framework that is known as the cost of carry model (TCS1 Model). The second method is based on the equivalent martingale measure theory (TCS2 Model) while the last approach is by using the partial differential equation approach (TCS3 Model). All of these three approaches are solved analytically based on the proposed terminal boundary condition of traded commodity salam to get the closedform formula. Finally, the proposed commodity salam models are being verified and validated. Two approaches have been considered in verification analysis which are the mathematical approach and the implementation of actual data graphically. Lastly, the performance analysis has been conducted on both types of salam models for validation purposes. The overall verification and validation results suggest that commodity salam models between two parties and the traded commodity salam model with 6% discount rate are the best models as compared to comparison models. Both types of salam models also satisfy the basic property of derivative theory which are the no risk and no arbitrage consideration as well as the convergence property. Thus, with the development of the proposed commodity salam models, the main goal of this study has been achieved, which is to provide the new shariah compliance derivative products. Both types of proposed salam models not only can serve as the alternative to the existing conventional derivatives but these models are also useful as risk management tools. At the same time, the establishment of these models can fill the gap in Islamic derivative study and promote the growth of Islamic financial products.