Dynamic portfolio optimization with Credit Default Swaps

Shaunak S Dabadghao, Purdue University

Abstract

This dissertation studies Merton's optimal portfolio problem applied to an investor who trades in a Credit Default Swap (CDS). This work began under the guidance of Dr Capponi following his previous analysis Capponi and Figueroa [2011] with corporate bonds. We study the a portfolio optimization problem of a speculative investor allocating the wealth to an equity, a money market account and to a Credit Default Swap. This work is differentiated from Capponi and Figueroa [2011] since they analyze a portfolio of an equity, money market account and a zero-coupon corporate bond. The primary difference is our consideration of a CDS instead of a defaultable bond. Note that there is a significant difference in the reward structure of these two assets. The CDS has a continuous payment while the bond does not. Also, we consider the correlation between the CDS and the equity. Initially, we assume a market existing in a single regime and market coefficients are assumed to be constant. Under these assumptions, the dynamics of the CDS price are determined in terms of a stochastic differential equation. The utility maximization problem is solved using a Hamilton-Jacobi-Bellman equation and verification theorems are shown for its solution. Explicit optimal strategies are obtained for an investor with a logarithmic utility function. With data from the last 150 years, we see that the corporate bond market suffers repeated clustered defaults. Since we are considering CDS that are written on corporate bonds, we incorporate this market behavior by modeling the economy to exist in multiple regimes. The market coefficients are assumed to depend on the regime in place. This regime is modeled by a nite state continuous Markov process. The CDS price dynamics is determined in terms of a Markov modulated stochastic differential equation and the Utility maximization problem is solved in the same way as above. Explicit optimal strategies are obtained for a logarithmic investor in a market that exists in 3 regimes. In the last chapter, we extend the work done in Capponi and Figueroa [2011] to the situation where the assets are correlated with one another. Over the last 10 years, it has been observed that the credit markets and the equity markets are correlated. To incorporate this behavior, we model the default process as a doubly stochastic Poisson process where the default rate is a function of the stock price. The CDS price dynamics are determined as a function of the stock price and the utility maximization problem is solved in a similar fashion. Explicit strategies are obtained for a logarithmic investor. We see that the optimal investment in the CDS and stock are dependent on each other.

Degree

Ph.D.

Advisors

Morin, Purdue University.

Subject Area

Finance|Industrial engineering|Operations research

COinS