Bivariate semi-Markov reward chain and credit spreads

D’Amico, Guglielmo; Manca, Raimondo; Salvi, Giovanni E.

doi:10.1093/imaman/dpv009

Cited by 3 publications

(3 citation statements)

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“…The above publications of non-homogeneous semi-Markov and Markov renewal processes for credit risk was followed by quite a lot of literature by the same and other authors in credit risk and related subjects. For example, from recent years, see Huang [13], D' Amico et al [14,15], D' Amico [16], Magni et al [17], Wu et al [18,19], Puneet et al [20], De Blasis [21]. In D' Amico et al [22], bivariate semi-Markov processes are introduced for the pricing of Credit Default Swaps (CDS).…”

Section: Introductionmentioning

confidence: 99%

Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Vassiliou

2020

Mathematics

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For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

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Section: Introductionmentioning

confidence: 99%

Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Vassiliou

2020

Mathematics

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“…The influence of rating dynamics on the credit spread evolution has been highlighted in financial literature by [10] and [21], mainly concerning industry sector. Another source of dependence for the credit spread evolution can be found in [11]. In this work the authors proposed a bivariate semi-Markov reward approach to include the counterpart credit risk.…”

Section: Introductionmentioning

confidence: 99%

“…11, 2002;March 30, 2009 and April 29, 2013. These findings are supported by the results of statistical test Λ at a significance level of 0.05 as shown in Table(5) To compute the expected Results of the statistical test: Λ 0.95 stems from the bootstrap simulation; Λ is the statistic computed on the observed data.…”

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confidence: 97%

A Copula-based Markov Reward Approach to the Credit Spread in the European Union

D’Amico

Petroni

Regnault

et al. 2019

Applied Mathematical Finance

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In this paper, we propose a methodology based on piecewise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries' total spread allows understand any contagions in the EU. The methodology is applied to real data of 24 European countries for the three major rating agencies: Moody's, Standard & Poor's and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency and that the dependence structure is characterized by a strong correlation between most of European countries.

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2017

Semi‐Markov Migration Models for Credit Risk

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Bivariate semi-Markov reward chain and credit spreads

Cited by 3 publications

References 27 publications

Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

A Copula-based Markov Reward Approach to the Credit Spread in the European Union

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