Structural Modelling of Credit Spreads on the European Bond Market: An Empirical Study

Abstract

This thesis empirically tests the explanatory power of structural models on the European corporate
bond market. Using new evaluation methods, including LASSO and gradient boosting regression,
we can provide an in-depth assessment of the models’ shortcomings. With these tools we show
that the structural models tend to systematically overstate or understate the spread due to an
oversensitivity to leverage ratio and asset volatility. We introduce a novel extension to the Black
Cox model in order to mitigate the observed weaknesses. Our extension is calibrated to match
historical default probabilities with an additional baseline default risk component attributable to
all firms. This approach manages to increase the R-squared from 39 % to 47 % and at the same
time reduce the residual dependencies of leverage ratio and asset volatility.

Popular Abstract (Swedish)

In a growing global corporate bond market, insights and understanding of the markets pricing mechanisms becomes increasingly important to investors. While previous research on credit risk has mainly focused on the American bond market, European bonds remain rather unexplored in academia. In this article, we investigate the explanatory power of a family of credit risk models - called structural models - applied on the European corporate bond market. Using new methods of model evaluation on a dataset of over 50 000 observations, we derive a novel extension to existing models yielding improved explanatory power compared to the base case.
WHAT IS A BOND?
Companies in need of financing can besides from raising capital through bank loans, issue bonds to investors. A bond is a contractual agreement, in which a firm promises investors to receive future payments in exchange for an upfront payment at the date of issue. From the issuers point of view, a bond can finance projects and activities that are too large and risky for a single bank to fund alone. Instead capital and risk is pooled among several investors owning a smaller share of the debt. From the investors perspective, the upside of a bond investment is that the returns of promised future cash flows often exceed the interest rate of a risk-free investment. Due to the complex nature of corporate debt, the translation of bond characteristics to market price is not straightforward. Research has therefore historically focused on trying to describe prices on the market through different theoretically founded models.
STRUCTURAL MODELS AND BEYOND
The structural approach is by many regarded as the most successful framework thanks to its intuitive interpretation of credit risk. The general structure of the structural framework assumes that corporate debt is valued as a contingent claim depending on the total value of the issuing firm, which evolves as a stochastic process. The analogy to option pricing derives from the fact that debt holders are prioritised higher than equity holders in terms of repayment. Imagine a firm active only during one year and liquidated at the end of that year. If the firm remains solvent until liquidation, debt holders are repaid the nominal amount of debt. However, if the firm is defaulted at the year-end, debt holders are repaid the residual firm value after bankruptcy costs. Within the structural framework we have mainly fo
cused on the Black Cox model, which allows the issuing firm to default not only when the bond contract is due, but at any time during the active period of the bond. Default occurs in the model if the firms value falls below a default boundary defined as a constant multiplied by the issued amount of debt.
Boundary = d·(Tot. Debt), d ∈ (0,1] Using new evaluation methods, including modern machine learning algorithms, we show that the Black Cox model tends to systematically overstate or understate the bond price due to an oversensitivity with respect to the input parameters leverage ratio and asset volatility. Based on our findings we introduce the intercept calibrated leverage ratio model (ICLR) in which the default boundary is modified slightly as
Boundary = m + d·(Tot. Debt), m ∈ (0,1], d ∈ (0,1] The essence of this structure is that we introduce a common risk component for all firms. This modification is in many ways intuitive since an IT-company with 20 % leverage ratio may have bonds traded at higher spreads than a highly levered real-estate company. Exploring the models oversensitivity to asset volatility we find - rather surprisingly - that only 13 % of the instantaneous asset volatility is attributable to the valuation of bond prices. As a consequence, the model performs better when assuming a constant asset volatility over time. With the original Black Cox model as base case, we improve the R-squared from 39 % to 47 % when implementing ICLR and constant asset volatility. The residuals from our final model also show decreased dependence of leverage ratio and asset volatility. However, these input parameters along with the risk-free interest rate and payout ratio remain influential. This result hints that the structural models are not fully capable of absorbing the default risk components of European corporate bond prices. Other remaining dependencies are found to originate from the bid ask spread, the size of the bond issue in relation to total debt, the US federal swap rate and the market capitalisation as a few examples. Ultimately, the dependency analysis show that other factors which are not considered in the structural models affect price levels on the European bond market. These factors are considered as non default components, which rather relate to liquidity, political, inflation and supply risks. Further research should therefore focus on finding theoretically backed models of disaggregating default and nondefault components in the observed yield spreads. This will result in other model evaluation frameworks, which can better assess and compare the explanatory ability of structural models.

• author: Zethraeus, Marcus and Roos, Magnus
• supervisor: Erik Lindström
• organization: Mathematical Statistics
• course: FMS820 20171
• year: 2017
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: Structural models, Merton model, Black Cox model, European corporate bond spreads
• language: English
• id: 8915339
• date added to LUP: 2017-06-14 10:41:59
• date last changed: 2017-06-14 10:41:59