Levy随机桥与金融信息建模

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摘要翻译：
Brody、Hughston和Macrina(BHM)的基于信息的资产定价框架被扩展到包括更广泛的市场信息模型。在BHM框架中，每个资产都与随机现金流的集合相关联。资产的价格是现金流的贴现条件预期的总和。条件期望是相对于由一组“信息过程”产生的过滤而取的。这些信息过程携带着关于现金流量的不完全信息。为了对信息流进行建模，本文引入了一类过程，我们称之为Levy随机桥(LRBs)。这个类推广了BHM所考虑的布朗桥和伽马桥信息过程。LRB是在有限的时间范围内定义的。根据其最终价值，LRB在法律上与Levy Bridge相同。我们详细考虑资产产生单个现金流$x_t$发生在固定日期$t$的情况。关于$x_t$的市场信息流是由一个终止于日期$t$的LRB建模的，该LRB的（随机）终端值等于$x_t$。通过求出相对于LRB的自然过滤的贴现条件期望x_t$,得到了此类资产价格过程的显式表达式。这种资产的欧式期权的价格是计算出来的。
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英文标题：
《Levy Random Bridges and the Modelling of Financial Information》
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作者：
Edward Hoyle, Lane P. Hughston, Andrea Macrina
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  The information-based asset-pricing framework of Brody, Hughston and Macrina (BHM) is extended to include a wider class of models for market information. In the BHM framework, each asset is associated with a collection of random cash flows. The price of the asset is the sum of the discounted conditional expectations of the cash flows. The conditional expectations are taken with respect to a filtration generated by a set of "information processes". The information processes carry imperfect information about the cash flows. To model the flow of information, we introduce in this paper a class of processes which we term Levy random bridges (LRBs). This class generalises the Brownian bridge and gamma bridge information processes considered by BHM. An LRB is defined over a finite time horizon. Conditioned on its terminal value, an LRB is identical in law to a Levy bridge. We consider in detail the case where the asset generates a single cash flow $X_T$ occurring at a fixed date $T$. The flow of market information about $X_T$ is modelled by an LRB terminating at the date $T$ with the property that the (random) terminal value of the LRB is equal to $X_T$. An explicit expression for the price process of such an asset is found by working out the discounted conditional expectation of $X_T$ with respect to the natural filtration of the LRB. The prices of European options on such an asset are calculated.
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PDF链接：
https://arxiv.org/pdf/0912.3652

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