Three Essays on Contingent Claims Pricing
Three Essays on Contingent Claims Pricing
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关于或有债权定价的三篇论文
DOI：
10.2139/ssrn.906146
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Anlong Li
中科院分区：
文献类型：
--
作者：
Anlong Li
本论文围绕当代金融期权定价理论及其应用的三个方面展开研究。这些主题的共同主题涉及金融债权的定价，其价值成为路径依赖时，使用通常的格逼近计划。第一篇文章探讨了潜在的转换和其他计划，在构建一个简单的二项式过程，弱收敛到所需的扩散限制序列。当标的资产价格用简单的二项式过程近似时，建立了欧洲和美国或有债权估值的收敛性结果。它还演示了如何构造反射或吸收二项式过程近似扩散边界。数值算例表明，所提出的简单近似方法不仅收敛，而且比已有的方法（如纳尔逊和Ramaswamy（1990））给出的结果更精确，特别是对于较长的到期日。我们在第二篇文章中的目的是双重的。首先，我们扩展了一些简单的一维扩散的晶格近似方法，以更高的维度和特殊的晶格近似完美的相关扩散。然后，我们研究当前的建模问题的利率期限结构，并演示如何应用这里开发的近似技术来处理这些模型中的路径依赖和多来源的不确定性。最后分析了固定利率存款保险下投保银行的投资决策。该模型考虑了特许权价值，并允许银行动态修改其资产组合。在保留特许权和利用存款保险之间存在权衡。最优银行投资组合问题的解决解析为一个常数的特许权价值。在任何审计期间，银行在某个关键时刻之前最大化其风险敞口，之后谨慎行事。相应的存款保险被证明是一个看跌期权，在这个关键时刻到期，而不是在审计日期。
This dissertation consists of three research topics in contemporary financial option pricing theories and their applications. The common theme of those topics involves the pricing of financial claims whose value become path-dependent when using the usual lattice approximating schemes. The first essay explores the potential of transformation and other schemes in constructing a sequence of simple binomial processes that weakly converges to the desired diffusion limit. Convergence results are established for the valuation of both European and American contingent claims when the underlying asset prices are approximated by simple binomial processes. It is also demonstrated how to construct reflecting or absorbing binomial processes to approximate diffusions with boundaries. Numerical examples demonstrate that the proposed simple approximations not only converge, but also give more accurate results then existing methods such as Nelson and Ramaswamy (1990), especially for longer maturities. Our purpose in essay 2 is two-fold. First we extend some of the simple lattice-approximation methods for one-dimensional diffusions to higher dimensions and develop special lattices to approximate perfectly correlated diffusions. We then examine current modelling issues of the term structure of interest rates, and demonstrate how to apply the approximation techniques developed here to handle path-dependence and multi-sources of uncertainty in these models. The last essay analyzes the investment decisions of insured banks under fixed-rate deposit insurance. The model takes into account the charter value and allows banks to dynamically revise their asset portfolios. Trade-offs exists between preserving the charter and exploiting deposit insurance. The optimal bank portfolio problem is solved analytically for a constant charter value. In any audit period, banks maximize their risk exposure before some critical time and act cautiously thereafter. The corresponding deposit insurance is shown to be a put option that matures at this critical time rather than at the audit date.