Abstract
In this paper, we make a comprehensive credit risk analysis on government bonds (GBs) of Germany, France, Italy, Spain and Greece over the period 2007.4–2012.3, where interest rate (IR) differential, GB price differential, default probability (DP) and credit default swap (CDS) are considered. First, applying the GB-pricing model in Kariya (Quantitative methods for portfolio analysis: MTV approach. Springer, Berlin, 1993) to these GB prices, we derive the term structures of interest rates (TSIRs) and discuss on the Maastricht convergence condition for the IR-differentials among these states relative to the German TSIRs and make some observations on some divergent tendencies. The results are associated with the business cycles and budgetary condition of each state. In the second part, to substantiate this viewpoint, we first make credit risk price spread analysis on price differentials and derive the term structures of default probabilities (TSDPs) of the French, Italian, Spanish and Greek GBs relative to the German GBs, where the corporate bond (CB) model proposed in Kariya (Advances in modern statistical theory and applications: a Festschrift for Professor Morris L. Eaton. Institute of Mathematical Statistics, Beachwood, 2013) is used in the derivation. Then it is empirically shown that the TSDPs show a significant divergent movement at the end of 2011, affected by the Euro Crisis. In addition, the TSDPs of these GBs are empirically shown to be almost linear functions of the differences of the TSIRs, which enables us to state the Maastricht condition in terms of DP. Thirdly the effectiveness of our TSDPs is empirically verified by comparing them with the corresponding CDSs against US dollars.
Highlights
The Financial Crisis in 2008–2009 and the European Crisis thereafter made many European states in the the European Economic and Monetary Union (EEMU) confronting severe budgetary and unemployment problems, as reflected in Greek economy
Since these government bonds (GBs) are of common currency unit “euro”, the bonds issued by the EEMU states are substitutable from investors’ viewpoint and the price differentials observed in the GB markets basically show the substitutable rates or equivalently credit risks in euros, which is made by alert and sensitive investors
To derive term structures of interest rates (TSIRs), the forward-looking GB-pricing model proposed in Kariya (1993) and applied in Kariya et al (2012) is applied to each monthly cross-sectional set of GB prices
Summary
The Financial Crisis in 2008–2009 and the European Crisis thereafter made many European states (countries) in the the European Economic and Monetary Union (EEMU) confronting severe budgetary and unemployment problems, as reflected in Greek economy. Is used to look forward over a future term with concept of DP for those firms that have not defaulted These current market prices are supposed to reflect and include investors’ views, projection and perspectives on future economic and financial movements or budgetary conditions of firms or states over a future term, given past time series information. To derive TSDPs relatively to DGB, the forward-looking CB (Corporate Bond) pricing model proposed in Kariya (2013) is applied to each monthly cross-sectional set of FGB, IGB, SGB, and GrGB, which are regarded as CBs in the model, while DGBs are viewed as non-defaultable reference GBs. In derivations of TSIRs, P-differentials and TSDPs, we use each monthly crosssectional set of GB price data, where price data is observed at the last business day of each month and the period of analysis is 2007.4–2012.3. We take a price approach to measuring TSIRs, CRIPSs and TSDPs through GB price model, where TSIR and TSDP are approximated by polynomials
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