Likviditetsanalyse med Konstant og Stokastisk Recovery i et Affint Modelsetup

Josefine Lund Christiansen & Karina Christiansen Nyborg

Student thesis: Master thesis


In this master thesis we examine the size of liquidity in U.S corporate bonds before, during and after the Financial Crisis 2007-2009 based on two different model approaches. Our first model approach is to assume constant recovery. In the second model approach we extend the model to handle stochastic recovery. Our theoretical pricing framework is based on (Duffie et al., 2000) and (Chen og Joslin, 2012). Based on the work of (Duffie et al., 2000) we derive closed form solutions in the setting of affine jump-diffusion state processes for conditional expected values for two choices of payoff functions. Based on (Chen og Joslin, 2012) we expand the conditional expected values for which we also find closed form solutions. We assume that the Credit Default Swap-premium (CDS-premium) is 100% liquid and therefore can be used as a proxy of credit risk in the credit spread. Based on the theoretical pricing framework we extract the instantaneous default intensity from the CDS-premium and the instantaneous liquidity measure is hereafter extracted from the corporate bond price. We use CDS-data and corporate bond data for Investment Grade companies in the period 2006-2013. Based on the extracted default intensities and the liquidity premium we compare the two model approaches and find small indications that the model in which we assume a constant recovery overestimates the instantaneous default intensities for moderate default intensities. Based on our dataset we are however not able to determine whether the overestimation is significant.We conclude that an analysis on another dataset is in place and suggest that a similar analysis is done for a more high risk dataset such as companies from the High Yield index. Based on the extracted default intensities and the liquidity measure we conduct a liquidity analyses based on a decomposition of the credit spread. From this we find that the credit spread in general is low before the Financial Crisis, increases during the Financial Crisis and falls to a lower level after the Financial Crisis but not to the same levels as seen before the crisis. The decomposition shows how much of the credit spread that is due to liquidity. From the decomposition we see that before the crisis the credit spread consisted of only credit risk. During the Financial Crisis this changed and about half of the credit spread was now explained by liquidity. After the Financial Crisis the liquidity has fallen and now only explains about 25% of the credit spread. From this we conclude based on our dataset that the most important element in driving up the credit spread to the high levels seen during the Financial Crisis was liquidity. We also conclude that the credit spreads are not at the same levels as before the Financial Crisis and there is in fact still a significant amount of liquidity represented in the credit spread. At last we discuss the most important assumptions where we conclude that the model with stochastic recovery is more sophisticated but also far more computationally complex.

EducationsMSc in Mathematics , (Graduate Programme) Final Thesis
Publication date2013
Number of pages148