Pricing of collateralized debt obligations and credit default swaps using Monte Carlo simulation

Abstract

The recent economic crisis has been partially blamed on the decline in the housing market. This decline in the housing market resulted in an estimated 87% decline in value of collateralized debt obligations (CDOs) between 2007 and 2008. This drastic decline in home values was sudden and unanticipated, thus it was incomprehensible for many investors how this would affect CDOs. This shows that while analytical techniques can be used to price CDOs, these techniques cannot be used to demonstrate the behavior of CDOs under radically different economic circumstances. To better understand the behavior of CDOs under different economic circumstances, numerical techniques such as Monte Carlo simulation can be used instead of analytical techniques to price CDOs. Andersen et al (2005) proposed a method for calculating the probability of defaults that could then be used in the Monte Carlo simulation to price the collateralized debt obligation. The research proposed by Andersen et al (2005) demonstrates the process of calculating correlated probability of defaults for a group of obligors. This calculation is based on the correlations between the obligors using copulas. Using this probability of default, the price of a collateralized debt obligation can be evaluated using Monte Carlo simulation. Monte Carlo simulation provides a more simple yet effective approach compared to analytical pricing techniques. Simulation also allows investors to have a better understanding of the behaviors of CDOs compared to analytical pricing techniques. By analyzing the various behaviors under uncertainty, it can be observed how a downturn in the economy could affect CDOs. This thesis extends on the use of copulas to simulate the correlation between obligors. Copulas allow for the creation of one joint distribution using a set of independent distributions thus allowing for an efficient way of modeling the correlation between obligors. The research contained within this thesis demonstrates how Monte Carlo simulation can be used to effectively price collateralized debt obligations. It also shows how the use of copulas can be used to accurately characterize the correlation between obligor defaults for pricing collateralized debt obligations. Numerical examples for both the obligor defaults and the price of collateralized debt obligations are presented to demonstrate the results using Monte Carlo simulation.