A Three-Factor Defaultable Term Structure Model

Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility

A four‐factor model (the extended model of Schmid and Zagst) is presented for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is an advancement of an earlier three‐factor model. In addition to a firm‐specific credit risk factor, a new systematic risk factor in the form of GDP growth rate is included. This new model is set in the context of other hybrid defaultable bond pricing models and empirically compared to specific representatives. We find that a model based only on firm‐specific variables is unable to capture changes in credit spreads completely. However, it is shown that in this model, market variables such as GDP growth rates, non‐defaultable interest rates and firm‐specific variables together significantly influence credit spread levels and changes.

this paper we present a tree model for defaultable bond prices which can be used for the pricing of credit derivatives. The model is based upon the two-factor Hull-White (1994) model for default-free interest rates, where one of the factors is taken to be the credit spread of the defaultable bond prices. As opposed to the tree model of Jarrow and Turnbull (1992), the dynamics of default-free interest rates and credit spreads in this model can have any desired degree of correlation, and the model can be fitted to any given term structures of default-free and defaultable bond prices, and to the term structures of the respective volatilities. Furthermore the model can accommodate several alternative models of default recovery, including the fractional recovery model of Duffie and Singleton (1994) and recovery in terms of equivalent default-free bonds (see e.g. Lando (1998)). Although based on a Gaussian setup, the approach can easily be extended to non-Gaussian processes that avoid negative interest-rates or credit spreads

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Hedging with Interest Rate and Credit Derivatives by Banks

Merton model has provided a classic theoretical framework for explaining credit spreads. This paper extends Merton model by introducing morphology factor of asset value volatility in the model, and conducts empirical studies on the effect of asset volatility morphology on credit spreads in China’s bond market. The results show that asset volatility morphology is economically important and can explain credit spreads well. Furthermore, this paper analyzes the asymmetric influences of monetary policy on credit spreads and asset volatility morphology. This paper points out that the responses of credit spreads and asset volatility morphology to monetary policy are consistent in the tight liquidity environments. To this end, monetary policy and liquidity, which are two factors that have been ignored by classic Merton model but proved to have significant influences on credit spreads, play roles in influencing credit spreads by changing volatility morphology of asset value. Since asset volatility morphology can reflect the change of investors’ expectation on the default probability of asset, the argument mentioned in the credit spread puzzle that the fundamentals related to bond default probability cannot explain credit spreads needs to be reexamined.

Poor liquidity of corporate bonds in emerging markets deters reliable estimation of credit spreads. As an alternative, credit spreads based on poll data are introduced in India. These spreads are used for pricing new credit instruments and for valuation of bond portfolios. We examine the credit risk characteristics of these spreads based on the structural models of bond pricing. We find that the spreads are largely deter-mined by the proxies of default probability and recovery rate. Also, the relation between spreads and important credit risk variables is as predicted by the models. These results support the use of poll-based credit spreads. Introducing poll-based spreads in less liquid corporate bond markets is likely to offer a reliable basis for pricing credit instruments and derivatives.

Are Credit Spreads and Interest Rates Co-Integrated? Empirical Analysis in the USD Corporate Bond Market

Credit Derivatives and Bank Credit Supply

Modelling the Evolution of Credit Spreads using the Cox Process within the HJM Framework: A CDS Option Pricing Model

This paper shows that credit default swaps (CDS) can affect the type of debt firms issue. Firms face a trade‐off between investment scale and the cost of capital measured by the credit spread. Small‐scale investment is safe, fully collateralized, but earns modest profits in all states. Large‐scale investment is risky, requires a positive credit spread, but yields high profits only in good states and default in bad states. CDS only affect risky credit spreads, which in turn affects the opportunity cost of issuing collateralized, safe debt. Covered (Naked) CDS lower (raise) credit spreads and raise (lower) the likelihood of issuing risky debt. Finally, we show that CDS generate credit spread and investment spillovers for non‐CDS‐referenced firms.

Purpose: This study examines the relationship between Environmental, Social, and Governance (ESG) integration and the cost of capital for Microsoft Corporation from 2015 to 2025, analyzing how comprehensive sustainability initiatives influence borrowing costs, credit ratings, and investor valuations. Methodology: Employing a mixed-methods longitudinal case study design, this research combines quantitative analysis of financial metrics (bond yields, credit spreads, cost of debt) with qualitative thematic analysis of ESG initiatives. Secondary data sources include Microsoft's annual reports (2015-2025), sustainability disclosures, credit rating reports, and market data from Bloomberg and Refinitiv databases. Findings: Microsoft's ESG integration strategy correlates strongly with favorable cost of capital outcomes, including maintenance of AAA credit ratings across all major agencies, bond yields approaching Treasury rates (spread compression to 8 basis points), and statistically significant negative correlations (r = -0.82, p < 0.001) between ESG performance scores and cost of debt. The company's carbon-negative commitment, water-positive initiatives, and circular-economy programs demonstrate measurable financial value creation by reducing financing costs. Implications: Findings validate the business case for strategic ESG integration, demonstrating that proactive sustainability investments create quantifiable financial value by reducing capital costs. Microsoft's framework provides actionable insights for technology firms seeking to optimize capital structures through ESG excellence. Originality: This research addresses the limited empirical evidence on ESG-cost of capital dynamics within the technology sector, providing a longitudinal analysis of the sole major corporation maintaining universal AAA ratings while executing transformative sustainability commitments. Limitations and directions for future research: A single-case design limits generalizability across industries and firms with different resource endowments. Future research should pursue comparative technology-sector analysis and longitudinal studies extending beyond 2030 to capture the full impact of realization.

Do Credit Spreads Reflect Stationary Leverage Ratios? Reconciling Structural and Reduced-Form Frameworks

Realized jumps on financial markets and predicting credit spreads

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of many credit derivatives and collateralized debt obligations. A simple and tractable intensity-based model predicts correlated defaults in which unpredictable default arrival times are jointly exponentially distributed. All relevant results are given in closed form, so the model can be easily implemented. The efficient simulation of dependent default times for pricing and risk management purposes is straightforward as well. Parameter calibration relies on market data as well as data from the rating agencies and credit risk management solutions.