Mathematical Modeling of Sukuk

Abstract

Data on sukuk issued so far shows that the majority of these have fixed coupon payments, which is equivalent to interest bearing fixed coupon bonds. Two mathematical models are reviewed that are proposed for risk-sharing and profit-sharing sukuk that is consistent with the principles of Islamic finance. The proposed sukuk are debt instrument – with stochastic coupons that depend on proxies for the profitability of the issuing firm. The first model is applicable to a sukuk with the issuer depending on a commodity like oil that has a transparent index for its price. An index-linked coupon bond, which is equivalent to a sukuk, pays coupons with values that are stochastic – depending on a market defined index – and has been proposed in Belal Ehsan Baaquie (2018a), Belal Ehsan Baaquie (2018b). The proposed model is studied by taking the index of the coupons to be based on the price of oil, given by Brent Crude Oil Index. In particular, a case study is reviewed by comparing fixed coupon bonds issued Petronas are compared with their corresponding sukuk with index-linked coupons Belal Ehsan Baaquie (2023). The second model is for sukuk issued by publicly listed firms; the coupons depend on the valuation of the issuing firm, which is taken to be a proxy of its profitability Belal Ehsan Baaquie (2020b), Belal Ehsan Baaquie (2020a). An empirical analysis of valuation based sukuk is reviewed to see its comparison with fixed coupon bonds Belal Ehsan Baaquie and Muhammad Mahmudul Karim (2022).