Research On The Pricing Of Islamic Bonds Based On PDE Method

In the world financial crisis of 2008,Islamic bond,based on the physical basis,is the relative winner,and the regressive growth under the crisis makes it come into the eyes of investors.Islamic bonds,also known as sukuk,are an important part of Islamic finance.It restricted by Islamism refuse the interest,oppose speculation and uncertainty,as well las initiator and holder share profits and risks.Therefore,Islamic bonds establish its own system in laws,regulations,distribution,su-pervision system,etc.On one hand,strict audit makes Islamic bond price be higher than ordinary bonds,on the other hand,Islamic bond price has more stronger ability to resist risks than ordinary bonds.The development of Islamic bond in China is helpful to the implementation of strategy of"the Belt and Road",and good for the development of Xinjiang,and beneficial for improving our socialistic market economy system.So we need to have a clear understanding and control on its risk and returns in the financial market.The thesis is about the pricing of the Islamic bond.Islamic bond,as a bond based on the physical assets property,can't directly hedge its un-derlying asset to complete pricing.This thesis first makes analysis on the operating mechanism of the rental Islamic bond and reaches a conclusion that the price of Islamic bond comes from the price and the rental income of the house estates.For the price of the house estates,we have transformed it into European options and solved with partial differential.For the rental incomes,we have adopted the formula Feynman-Kac to get the partial differential equation it satisfies and finally we get the numerical solution with finite difference method.Secondly,for the hedge risk of the unsellable house estate asset which is tagged by the Islamic bond,the thesis has selected the property price-related house price to hedge partial risk.So that the investor has the rights to get possible supernormal profit.The value function is defined with the target that the no matter the investor has brought the Islamic bond and he or she can realize the maximum expected utility until the due date with the adoption of the method of indifference in utility,meaning from the in-vestor's viewpoint.And then HJB equation is deduced with the dynamic programming principle.Finally,the analytical solution of the indifference price of Islamic bond is attained with the help of elementary solution.At last because lots of researches have proven that securities market doesn't total follow the standard Brownian motion and have much characteristic of fractional Brownian motion.So with assumption of fractional Brownian motion,we make furtherly pricing research on the Islamic bond which could be terminated earlier and the price without difference in utility of this Islamic bond is achieved with the method of indifference in utility.