Mathematical modelling and evaluation of the Islamic derivative Arbun

Abstract EN

Options are derivatives, meaning they derive their value from an underlying financial instrument.

Though options can be entered using stock as the underlying security, indexes and futures also have options available.

Options are an extremely versatile instrument and can be used to create a variety of different limited risk strategies.

In Islamic finance, these products are not used because their principles are not consistent with the principles of the Islamic Sharia’a.

However, there are derivatives that are equivalent to the latter and which may be subject to assets risk management.

Among these Islamic products we have “Arbun”, this one not often used in reality because of the difficulty of its evaluation as there is no mathematical model that can describe it.

In this context and in order to overcome this issue, we present in this paper a new mathematical approach to model the derivative “Arbun” based on stochastic processes and genetic algorithms.

The main purpose of this approach is to offer a decision tool to investors to control the market risk in Islamic finance.