随机利率下期权定价分析与模拟

发布时间：2018-01-15 08:03

本文关键词：随机利率下期权定价分析与模拟　出处：《山东大学》2012年硕士论文　论文类型：学位论文

【摘要】：在利率市场化日益推进的今天,利率的波动带来的风险对各国的金融市场影响越来越大,将利率风险纳入系统风险的考虑范围显得尤为必要。在经典的B-S公式当中,我们假设利率是确定性的,因而在上面的大背景下,再利用经典的B-S公式来考虑问题,误差会显得比较高,在某些情况下可能会存在严重的危险。本文仍然以经典的B-S公式为基础进行讨论,在此基础上再假设利率满足Hull-White模型(我们会在文中介绍到使用这个利率模型的几个优点),即(4.1)式,这样加上标的资产也满足一个SDE,我们便有了两个布朗运动Wt与Wt0。本文的主体思路便开始于此,鉴于我们对这两个布朗运动并没有先前的假设,我们从下面三种情形开始讨论,首先给出两过程二次变差的定义,此即(4.2)式。从这个切入点我们分别对ρ=0；ρ=1；以及其它情形三种情况分别得出新型的B-S公式。在前两种情形中,我们在实际中都有相关的产品对应,因此这显得更加容易理解。而对于其它情形的讨论,虽然在实际中我们没有直观的产品,但它的定价过程非常自然的程度完全可以用来构造一种新的金融产品。在有了这些新的B-S公式之后,我们发现它们和经典的B-S公式有很大程度的相似之处,于是我们便进一步想到它们可能也有类似与经典的二叉树的数值模拟方法。所以在最后一章里,我们着重讨论了前面所提到的两种情形的二叉树模拟方法(由于第三种在实际中并没有对应的产品,我们不予讨论)。分析的结果显示在随机利率的假设下,确实有类似于经典二义树的模拟方法,并且我们用Matlab来对其进行了模拟,得到了满意的结果。
[Abstract]:With the development of interest rate marketization, the risk of interest rate fluctuation is becoming more and more important to the financial markets of various countries. In the classical B-S formula, we assume that the interest rate is deterministic, so under the background above. Then using the classical B-S formula to consider the problem, the error will appear to be relatively high, and in some cases there may be serious danger. This paper is still based on the classical B-S formula. On this basis, we assume that the interest rate satisfies the Hull-White model (we will introduce several advantages of using the interest rate model in this paper, that is, 4. 1). If the underlying assets satisfy an SDE then we have two Brownian motions WTT and Wt0.The main idea of this paper begins here since we do not have previous assumptions about these two Brownian motions. We start with the following three cases. First, we give the definition of quadratic variation of two processes, which is called the form of 4.2). 蟻 1; In the first two cases, we have the relative product correspondence in practice, so it is easier to understand. Although there is no intuitive product in practice, its pricing process is very natural enough to be used to construct a new financial product. With these new B-S formulas, we find that they are very similar to the classical B-S formulas. Then we thought that they might also have numerical simulations similar to those of the classical binary trees, so in the last chapter. We focus on the binomial tree simulation method for the two cases mentioned above (since the third one has no corresponding product in practice, we do not discuss the results of the analysis under the assumption of stochastic interest rate. It is true that there is a simulation method similar to the classical binary tree, and we use Matlab to simulate it and obtain satisfactory results.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F820;F830.9

【共引文献】