A Structural Model For Credit Risk With Markov Modulated L Vy Processes And Synchronous Jumps

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A Structural Model For Credit Risk With Markov Modulated L Vy Processes And Synchronous Jumps

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Author : Donatien Hainaut
language : en
Publisher:
Release Date : 2014

A Structural Model For Credit Risk With Markov Modulated L Vy Processes And Synchronous Jumps written by Donatien Hainaut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Lévy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.

Credit Risk Modeling Valuation And Hedging

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Author : Tomasz R. Bielecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Credit Risk Modeling Valuation And Hedging written by Tomasz R. Bielecki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Business & Economics categories.

The motivation for the mathematical modeling studied in this text on developments in credit risk research is the bridging of the gap between mathematical theory of credit risk and the financial practice. Mathematical developments are covered thoroughly and give the structural and reduced-form approaches to credit risk modeling. Included is a detailed study of various arbitrage-free models of default term structures with several rating grades.

Credit Risk Modeling

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Author : Ayhan Yuksel
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2010

Credit Risk Modeling written by Ayhan Yuksel and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

This book deals with the modeling of credit risk by using a structural approach. Three fundamental questions of credit risk literature are analyzed throughout the book: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric Brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.

Structural Credit Risk Modeling With Jump Diffusion Processes Engl

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Author : Markus Pelger
language : de
Publisher:
Release Date : 2012

Structural Credit Risk Modeling With Jump Diffusion Processes Engl written by Markus Pelger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

Levy Processes In Credit Risk

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Author : Wim Schoutens
language : en
Publisher: Wiley
Release Date : 2009-08-28

Levy Processes In Credit Risk written by Wim Schoutens and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-28 with Business & Economics categories.

This book is an introductory guide to using Lévy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets - the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of Lévy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of Lévy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.

Semi Markov Migration Models For Credit Risk

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Author : Guglielmo D'Amico
language : en
Publisher: John Wiley & Sons
Release Date : 2017-06-01

Semi Markov Migration Models For Credit Risk written by Guglielmo D'Amico and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules. This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.

An Intensity Model For Credit Risk With Switching L Vy Processes

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Author : Donatien Hainaut
language : en
Publisher:
Release Date : 2014

An Intensity Model For Credit Risk With Switching L Vy Processes written by Donatien Hainaut and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. Firstly, as Lévy processes encompass numerous jump processes, our model can duplicate sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.

Structural Approach Of Credit Risk With Jump Diffusion Process

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Author : Thanh Binh Dao
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-07

Structural Approach Of Credit Risk With Jump Diffusion Process written by Thanh Binh Dao and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07 with categories.

"Structural Approach of Credit Risk with Jump Diffusion Process" proposes three essays in the modelling of the firm's asset value as a jump diffusion process within the structural approach of credit risk. The first essay deals with the modelling of a perpetual coupon debt structure using two different jump diffusion processes: double exponential and uniform. The second models a debt structure of roll-over perpetual, where the firm's asset value follows a double exponential jump diffusion process. The third develops a model with zero coupon debt structure, and takes into account a stopping time marked by an important negative jump. In our essays, we obtain almost closed form formulae for the debt, equity and firm values, as well as the endogenous default barrier and credit spreads. Levels of credit spreads obtained are closer to the market data and confirm the existence of an optimal capital structure, which takes into account the risk free rate, pay-out ratio, firm risk, tax rate, default costs, and jump intensity & sizes.These essays are designed to provide academic and practitioners with useful and insightful knowledge of credit risk, default event as well as credit spreada.

Credit Risk In Pure Jump Structural Models

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Author : Elisa Luciano
language : en
Publisher:
Release Date : 2006

Credit Risk In Pure Jump Structural Models written by Elisa Luciano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In particular, assuming a pure jump process. Moreover, when applied to market data diffusion-based structural models tend to produce too low spreads, even over longer horizons. In this paper we show that a jump process of the Variance-Gamma type for the asset value can also circumvent this practical shortcoming. We calibrate a terminal-default jump structural model to single-name data for the CDX NA IG and CDX NA HY components. We show that the VG model provides not only smaller errors, but also a better qualitative fit than other diffusive structural models. Indeed, it avoids both the spread underprediction of the classical Merton model and the excessive overpredictions of other well known diffusive models, as recently explored by Eom, Helwege, Huang (2004) or Demchuk and Gibson (2005).

Credit Correlation

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Author : Alexander Lipton
language : en
Publisher: World Scientific
Release Date : 2008

Credit Correlation written by Alexander Lipton and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Business & Economics categories.

The recent growth of credit derivatives has been explosive. The global credit derivatives market grew in notional value from $1 trillion to $20 trillion from 2000 to 2006. However, understanding the true nature of these instruments still poses both theoretical and practical challenges. For a long time now, the framework of Gaussian copulas parameterized by correlation, and more recently base correlation, has provided an adequate, if unintuitive, description of the market. However, the increased liquidity in credit indices and index tranches, as well as the proliferation of exotic instruments such as forward starting tranches, options on tranches, leveraged super senior tranches, and the like, have made it imperative to come up with models that describe market reality better. This book, originally and concurrently published in the International Journal of Theoretical and Applied Finance, Vol. 10, No. 4, 2007, agrees that base correlation has outlived its usefulness; opinions of how to replace it, however, are divided. Both the top-down and bottom-up approaches for describing the dynamics of credit baskets are presented, and pro and contra arguments are put forward. Readers will decide which direction is the most promising one at the moment. However, it is hoped that, in the near future, models that transcend base correlation will be proposed and accepted by the market. Sample Chapter(s). Introduction (31 KB). Chapter 1: L(r)vy Simples Tructural Models (209 KB). Contents: L(r)vy Simple Structural Models (M Baxter); Cluster-Based Extension of the Generalized Poisson Loss Dynamics and Consistency with Single Names (D Brigo et al.); Stochastic Intensity Modeling for Structured Credit Exotics (A Chaposvsky et al.); Large Portfolio Credit Risk Modeling (M H A Davis & J C Esparragoza-Rodriguez); Empirical Copulas for CDO Tranche Pricing Using Relative Entropy (M A H Dempster et al.); Pricing and Hedging in a Dynamic Credit Model (Y Elouerkhaoui); Joint Distributions of Portfolio Losses and Exotic Portfolio Products (F Epple et al.); On the Term Structure of Loss Distributions: A Forward Model Approach (J Sidenius). Readership: Professionals, academics and students in the areas of finance and bank