基于简约化模型定价的信用债券最优投资策略研究

发布时间：2018-02-26 05:33

本文关键词： 简约化模型信用债券最优投资策略随机控制方法鞅方法　出处：《上海交通大学》2012年博士论文　论文类型：学位论文

【摘要】：信用债券是依靠债券发行者的信用为基础发行的固定收益类金融工具，主要包括：企业债、公司债、中期票据、短期融资券、可转换债券、可分离债及资产支持证券等。信用债券是企业融资和金融市场投资的重要工具，其特殊的地位和性质已经逐步引起学术界的广泛关注和政府的高度重视。目前，国内外学者对信用债券的研究主要集中于定价领域，很少有文献涉及信用债券最优投资策略的研究。因此，对信用债券最优投资策略的研究，不仅可以在理论上丰富和完善动态投资组合理论，而且可以在实践中为投资者如何最优配置信用债券提供指导依据。本文主要从以下几方面对信用债券的最优投资策略进行了研究：（1）研究了跳跃风险溢价与信用债券最优投资策略之间的关系。在简约化模型的框架下，，对信用债券进行定价，并推导出其价格的动态过程。假设投资者的效用函数为对数效用函数和CRRA效用函数，利用随机控制方法得到了最优投资策略的解析解。结果表明：当投资者的效用函数为对数效用函数时，投资者对信用债券的最优投资策略只和跳跃风险溢价以及违约损失率有关，且只有当跳跃风险溢价大于1，即市场对跳跃风险进行风险补偿时，投资者才会持有信用债券，并且最优持有量随着跳跃风险溢价的增加而增加。当投资者的效用函数为CRRA效用函数时，投资者对信用债券的最优投资策略是跳跃风险溢价和投资期限的增函数，此外还是违约损失率和违约强度的减函数。（2）研究了当工资为一个随机过程时，企业年金如何对信用债券、股票以及银行存款进行最优配置的问题。假设企业年金的投资目标为基于最终财富的期望效用最大化，利用鞅方法得到了最优投资策略的解析解。结果表明：企业年金的最优投资策略由三部分组成，投机策略、工资的收入效应对冲策略以及工资的随机效应对冲策略。（3）假设投资组合中的信用债券之间的违约存在相关性，在随机利率的条件下研究了投资者配置于信用债券组合、国债、股票和银行存款的最优投资组合问题。利用简约化模型来刻画信用债券之间的违约相关性，并推导出各资产价格的动态过程；通过假设投资者的效用函数为CARA效用函数，利用鞅方法给出了此优化问题的解析解。结果表明：股票的最优投资策略与Merton问题的结果是一致的，国债的最优投资策略主要受利率风险溢价的影响，信用债券的最优投资策略相对复杂。当信用债券之间的违约相互独立时，某一信用债券的最优投资策略与其对应的冲击事件的跳跃风险溢价、违约损失率、违约强度、剩余投资期限以及风险规避系数有关。当信用债券之间的违约存在相关性时，某一信用债券的最优投资策略将受到与其相关的冲击事件的跳跃风险溢价、违约损失率、违约强度、剩余投资期限以及风险规避系数的影响，而且有可能出现被卖空的情况。本文的主要创新点：（1）揭示了跳跃风险溢价对信用债券最优投资策略的影响以往对信用债券最优投资策略的研究均基于投资者分散持有大量的相互独立的信用债券组合以满足“条件分散性”的假设下展开的。一个满足“条件分散性”假设的信用债券组合将不再具有跳跃风险（跳跃风险已被组合分散掉），因而，这些研究也就无法揭示跳跃风险溢价对最优投资策略的影响。实际上，一个满足“条件分散性”假设的信用债券组合并不存在，因为这个组合所要包含的债券数量需要趋近于无穷。大量的实证研究也表明跳跃风险溢价显著地存在于信用债券市场。因此，在现实中跳跃风险是投资者投资于信用债券时无法回避的风险。针对此不足，本文研究了一个代表性投资者投资于一个信用债券、股票以及银行存款时的最优资产配置问题。由于假设投资者仅投资一个信用债券，因而信用债券的跳跃风险依然存在，通过对其资产配置策略的研究，可以更好地理解跳跃风险溢价对信用债券最优投资策略的影响。（2）揭示了违约相关性对信用债券最优投资策略的影响已有文献对信用债券组合的最优投资策略进行了研究，但遗憾的是，为了模型的简便，这些文献均假设资产组合中信用债券之间的违约相互独立。但现实中，信用债券之间的违约往往并不是相互独立的，而是存在一定的违约相关性。为了使所研究的问题更符合实际，本文假设投资组合中的信用债券之间的违约存在相关性，在简约化模型的框架下，研究了随机利率条件下投资者配置于信用债券组合、国债、股票和银行存款的最优投资组合问题。将违约相关性引入至投资组合并揭示了其对最优投资策略的影响是本文与以往文献的另一显著不同和主要创新。（3）给出了非自融资策略下信用债券的最优投资策略目前有关信用债券最优投资策略的研究，均是以投资者的投资策略为自融资策略展开的，即假设投资者在投资期限内，除了初始财富外并没有额外的资金进出。这一关键性的假设显然不适合企业年金、养老基金、保险公司、开放式基金等机构投资者的投资策略。鉴于此，本文以企业年金为例，放松了自融资策略的假设，研究了企业年金对信用债券的最优投资问题，以丰富和完善企业年金最优资产配置策略以及信用债券最优投资策略的理论研究。
[Abstract]:Credit bond is a fixed income financial instruments, bond issuers rely on credit to issue mainly include: corporate bonds, corporate bonds, medium-term notes, short-term financing bonds, convertible bonds, bonds and asset-backed securities can be separated. The credit bond is an important tool for enterprise financing and financial market investment, its status and the special nature has gradually aroused a wide attention of government and academic circles.
At present, the research on credit bonds at home and abroad mainly focus on pricing field, there are few research literature related to optimal investment strategy for the defaultable bond. Therefore, the research on the optimal investment strategy for the defaultable bond, can not only enrich and perfect the dynamic investment portfolio theory in theory, but also can provide guidance for the investors to optimal allocation of credit the bond in practice.
This paper mainly studies the optimal investment strategy of credit bond from the following aspects:
(1) to study the relationship between the jump risk premium and the optimal investment strategy for the defaultable bond. In the framework of simplified model, the pricing of credit bonds, and deduced the dynamic process of its price. The utility function assumes that investors are logarithmic utility function and CRRA function, using the stochastic control method to obtain the optimal investment analysis solution. The results show that when the utility function of investors for the logarithmic utility function, the optimal investment strategy of credit bond investors only jump risk premium and default loss rate, and only when the jump risk premium is greater than 1, namely the market risk compensation for jump risk, investors will hold credit bonds, and the optimal holdings increased with the jump risk premium. When the utility function of investors for the CRRA utility function, the optimal investment strategy of credit bond investors It is an increasing function of the jump risk premium and the term of investment, in addition to the loss rate of default and the reduction function of the strength of default.
(2) studied when the salary is a stochastic process, the enterprise annuity to credit bonds, optimal allocation problems of stock and bank deposits. If the enterprise annuity investment to maximize the expected utility of the terminal wealth. Using the martingale method to derive the analytical solutions of the optimal investment strategy. The results show that the optimal the investment strategy of the enterprise annuity is composed of three parts, speculative strategy, hedging strategies of wage income effect and wages random effects of hedging strategies.
(3) assuming that portfolio of credit bonds default correlation between bonds in the stochastic interest rate is studied under the condition of investors configuration in the portfolio, credit bonds, the optimal portfolio of stock and bank deposits. Using the simple model to describe the default correlation between credit bonds, and deduced the dynamic process of each asset the price of the utility function; by assuming that investors for the CARA utility function, given the use of the martingale method and the analytical solution of this optimization. The results show that the stock of the optimal investment strategy and the Merton problem is consistent with the results, the optimal investment strategy of treasury bonds is mainly affected by the interest rate risk premium, the optimal investment strategy of credit bonds is relatively complex when the credit default bonds between the independent, impact events a credit bond optimal investment strategy and the corresponding jump risk premium, default The loss rate, default intensity, the remaining period of investment and risk aversion coefficient. When the default correlation between credit bonds, the optimal investment strategy of a credit bonds will impact the events related to jump risk premium, default loss rate, default intensity, influence of residual investment period and the coefficient of risk aversion, and likely to be short.
The main innovation points of this article are:
(1) the impact of jumping risk premium on the optimal investment strategy of credit bonds is revealed.
The past research on the optimal investment strategy for the defaultable bond investors are dispersed hold a large number of independent credit bond portfolio to meet the "condition based on dispersion under the hypothesis of expansion. A" meet the conditions of the dispersion of credit bond portfolio "hypothesis will no longer have the jump risk (jump risk portfolio has been so)., these studies did not reveal the effect of jump risk premium on the optimal investment strategy. In fact, a" meet the conditions of the dispersion of credit bond portfolio "hypothesis does not exist, because the number of bond portfolio to include the need to tend to infinity. A large number of empirical studies also show that the jump risk premium significantly in credit bonds in the market. Therefore, the jump risk investors to invest in credit bonds can not be avoided.
To solve this problem, this paper studied an investor to invest in a stock of credit bonds, bank deposits and the optimal asset allocation problem. Due to the assumption that investors invest only a credit bonds, and credit bonds jump risk still exists, through the study on the asset allocation strategy, you can better understand the effect of jump the risk premium on the optimal investment strategy for the defaultable bond.
(2) the influence of default relevance on the optimal investment strategy of credit bonds is revealed.
The optimal investment strategy of the portfolio credit bonds have studied the literature, but unfortunately, in order to model simple, these papers assume that default between credit bonds in a portfolio of assets are independent of each other. But in reality, the bond between the credit default are not independent of each other, but there is default correlation.
In order to make the study more practical problems, we assume that the default correlation between the portfolio of credit bonds exist in the framework of simplified model, studied under the condition of random interest rates investors configuration in the portfolio, credit bonds, the optimal portfolio of stock and bank deposits. The default correlation into investment portfolio and reveal its influence on the optimal investment strategy in this paper is from the previous literature a significantly different and the main innovation.
(3) the optimal investment strategy of credit bonds under non self financing strategy is given.
At present the research on the optimal investment strategy for the defaultable bond, are based on the investment strategy for investors to expand self financing strategy, assuming that investors in the investment period, except the initial wealth and no additional funds out. This hypothesis is not suitable for enterprise annuity, pension funds, insurance companies, institutional investors type of fund investment strategy. In view of this, based on the enterprise annuity as an example, relaxed self financing strategy that studies the optimal investment problem of credit bonds for enterprise annuity, in order to enrich and improve the enterprise annuity optimal asset allocation strategy and the optimal investment strategy for the defaultable bond theory research.

【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F830.91;F224

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