基于PDE方法的伊斯兰债券定价问题研究

发布时间：2017-12-31 21:08

本文关键词：基于PDE方法的伊斯兰债券定价问题研究　出处：《上海师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：2008年世界金融危机,基于实物基础的伊斯兰债券是相对赢家,危机下的逆行增长使其走入投资者的眼中.伊斯兰债券又称sukuk,是伊斯兰金融的重要组成部分.伊斯兰债券受伊斯兰教义限制拒绝利息,反对投机和不确定性以及发起方和持有人利润共享风险共担.因此伊斯兰债券在法规,发行,监管制度等方面自成体系.严格的审计与审核使得伊斯兰债券一方面售价高于普通债券,另一方面比普通债券有更强的抗风险能力.伊斯兰债券在我国的发行有利于“一带一路”战略的展开,有利于我国新疆地区的发展,有利于完善中国市场经济体系.因此我们需要对其在金融市场上的风险和收益有清醒的认识和精确的度量.本文是对伊斯兰债券定价问题的一次探究.伊斯兰债券是基于实物资产房产上的债券,无法直接对冲其标的资产来完成定价.本文首先分析租赁型伊斯兰债券的运行机制,得出伊斯兰债券的价格来源于标的资产房产价格和租金收益的结论.对于房产价格部分,我们复制成一份欧式期权,求解其满足的定解问题得出该部分的解析解;对于租金收益部分,我们应用Feynman-Kac公式得到其满足的偏微分方程,利用有限差分法得到数值解.其次,本文针对伊斯兰债券不能随意买卖标的资产房产来对冲风险,我们选用与房产价格有关的房屋价格指标来对冲部分风险.我们考虑一类具有放弃赎回条款的伊斯兰债券,使得投资人得到一份可能获得超额收益的权利.运用效用无差别的方法,即站在投资者角度,以投资者无论是否购买伊斯兰债券,到期日投资人实现期望效用最大化为目标定义值函数,接着根据动态规划原理推导出所满足的HJB方程,从而得到伊斯兰债券无差别价格的解析解.最后,由于大量研究证明证券市场并不完全遵循几何布朗运动,而是更服从于分数布朗运动.因此我们进一步在分数布朗运动的假设下,对于可提前终止的伊斯兰债券进行定价研究,并应用效用无差别方法得到了该类伊斯兰债券的效用无差别价格.
[Abstract]:In 2008, the world financial crisis, based on the physical basis of the Islamic bond is the relative winner, under the crisis of retrograde growth into the eyes of investors. Islamic bonds, also known as sukuk. Islamic bonds are an important part of Islamic finance. Islamic bonds are restricted by Islam to reject interest, oppose speculation and uncertainty, and share risks between sponsors and holders of profits. Therefore, Islamic bonds are regulated. Issuance, regulatory systems, and other aspects of the system. Strict audit and audit, on the one hand, the price of Islamic bonds higher than ordinary bonds. On the other hand, the issue of Islamic bonds in China is conducive to the development of "Belt and Road" strategy and the development of Xinjiang region. Therefore, we need to have a clear understanding and accurate measurement of the risks and returns in the financial market. This paper is an inquiry into the pricing of Islamic bonds. Bonds are bonds based on real assets, real estate. It is impossible to hedge the underlying assets directly to complete the pricing. Firstly, this paper analyzes the operating mechanism of leased Islamic bonds. It is concluded that the price of Islamic bonds is derived from the underlying asset property price and rental income. For the property price portion, we copy it into a European option. The analytic solution of this part is obtained by solving the satisfying definite solution. For the part of rent income, we use Feynman-Kac formula to obtain the partial differential equation and the finite difference method to obtain the numerical solution. This paper is aimed at sukuk bonds not to buy and sell the underlying assets and real estate as a hedge against risk. We use housing price indicators related to property prices to hedge some of the risk. We consider a class of Islamic bonds with foreclosure terms. To give investors a right to a potential excess return. Use a utility neutral approach, that is, from the investor's point of view, to investors whether or not to buy Islamic bonds. The expected utility maximization is defined as the objective value function, and then the HJB equation is derived according to the dynamic programming principle, and then the analytical solution of the indistinguishable price of the sukuk bond is obtained. As a large number of studies prove that the stock market does not follow the geometric Brownian motion completely, but is more comfortable with the fractional Brownian motion, so we further under the assumption of fractional Brownian motion. This paper studies the pricing of sukuk bonds which can be terminated in advance, and obtains the utility nondifferential price of the sukuk bonds by using the utility nondifferential method.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F831.51;F224

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