The Optimal Investment Strategy For Defaultable Bond: A Reduced Form Approach

Defaultable bond is a kind of fixed income instrument, which is to rely on the bond issuer credit, and mainly includes: Enterprise bonds, corporate bonds, medium‐term notes, short‐term financing bonds, convertible bonds, detachable bonds and asset‐backed securities. Defaultable bond is an important tool for corporate financing and investing, and its special characteristic and status have gradually aroused of academe and government's extensive attention.At present, domestic and foreign scholars who research on defaultable bond, mainly focus on the bond pricing. There are few literatures relating to the optimal investment strategy for defaultable bond. Therefore, the research on the optimal investment strategy for defaultable bond not only enriches and improves the investment portfolio theory, but also provides guidance for the investors to optimal allocation of defaultable bonds.In this paper, I study the optimal investment strategy for defaultable bond in the following aspects:(1) I research the relationship between the jump risk premium and the optimal investment strategy for the defaultable bond. I model the defaultable bond through the reduced‐form model and solve the dynamics of its price. Assuming the Logarithm and CRRA utility and using stochastic control methods, we obtain a closed‐form solution to the optimal investment strategy. The results show that when the utility is Logarithm utility, the optimal investment strategy for defaultable bond only depends on jump risk premium and default loss rate. For a jump risk premium greater than one, namely the market pricing the jump risk in the defaultable bond, the investor will optimally invest a positive amount in the defaultable bond; then, the optimal strategy for the defaultable bond is an increasing function of the jump risk premium. When the utility is CRRA utility, the optimal investment strategy for defaultable bond is an inreasing function of jump risk premium and investment horizon, and is a decreasing function of the loss rate and default intensity.(2) I research a defined‐contribution (DC) enterprise annuity how to optimally allocate her wealth among the following securities: a defaultable bond, a stock and a bank account, when the salary is a stochastic process. Assumed that the DC enterprise annuity's invest aim is to maximize the expected utility of the terminal wealth. Using martingale approach, obtained a closed‐form solution to this optimal problem. From the solution it is clear that enterprise annuity's optimal investment strategy for defaultable bond include three parts: one is the speculative strategy, another is the hedge strategy for salary income effect, and the other is the hedge strategy for salary stochastic effect.(3) I researched an investor how to optimally allocate her wealth among the following securities: defaultable bonds portfolio, the treasury, the stock and a bank account, when there is default correlation. Modeled the default correlation through a reduced‐form model and solved the dynamics of assets price. Assuming the unility is CRRA utility and using martingale method, obtained a closed‐form solution to this optimal problem. The results show that the optimal strategy for the stock is the same to Merton model. The optimal strategy for the treasury is mainly affected by interest rate risk premium. The optimal strategy for the defaultable bond is more complicate. When the defaultable bonds are independent each other, the optimal strategy for one of the defaultable bonds depends on the corresponding impact events' jump‐risk premium, loss rate, default intensity, and investment horizon. When the defaultable bonds are dependent each other, the optimal strategy for one of the defaultable bonds depends on associated impact events' jump‐risk premium, loss rate, default intensity, and investment horizon, and the defaultable bond could be short selling.The main innovations of this thesis:(1) I reveal impact of the jump risk premium on the optimal strategy for defaultable bondThe existing literature about the optimal investment strategy for defaultable bond assumed that the investors hold a large number of independent defaultable bonds portfolio to meet the conditional diversification assumption. Because the defaultable bonds portfolio diversifies jump risk, these studies did not analysis the impact of jump risk premium on optimal portfolio. But, in fact, if the market for defaultable bonds is thin, then the concept of conditional diversification does not hold. And growing empirical evidence supported the presence of jump risk premium in the defaultable security market. Therefore, the investors cannot evasive the jump risk when they invest in defaultable bonds.To solve the above problems, this paper studied an investor's the optimal investment strategy in a defaultable bond, a stock and a bank account in a continuous time model. Because I assume that the investor invest a defaultable bond, there is jump risk in defaultable bond. So I can find the relationships between the optimal amount invested in the defaultable bond and the jump risk premium.(2) I reveal impact of default correlation on the optimal strategy for the defaultable bondThere existed literatures about optimal investment strategy for the defaultable bonds portfolio, but it is pity that the exiting literatures have not considered the default correlation. The defaultable bonds are not independent of each other, but there is default correlation between the defaultable bonds.In order to make the study more practical, this paper researched researched an investor how to optimally allocate her wealth among the following securities: defaultable bonds portfolio, the treasury, the stock and a bank account, when there is default correlation.Bringing default correlation into investment portfolio and revealing its influence to optimal portfolio are key distinguishing features.(3) I give the optimal investment strategy for defaultab bond under non self-financial strategyThe existing literature about the optimal investment strategy for the defaultable bond assumes that the investor has a self‐financial strategy, namely in the investment horizon, the investors do not have additional fund except the initial wealth. This hypothesis is not suitable for the investment strategy of enterprise annuity, pension fund, insurance company, open‐end fund and so on. So, this paper looses the assumption of self‐financial, and researches the enterprise annuity how to optimally invest in the defaultable bond, to enrich and improve the theory of the enterprise annuity's optimal asset allocation strategy and the optimal investment strategy for defaultable bond.