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Author: Sanjiv Ranjan Das Publisher: ISBN: Category : Languages : en Pages : 37
Book Description
Modeling correlated default risk is a new phenomenon currently sweeping through the credit markets. In this paper, we develop a methodology to model, simulate and assess the joint default process of hundreds of issuers. Our study is based on a data set of default probabilities supplied by Moody's Risk Management Services. We undertake an empirical examination of the joint stochastic process of default risk over the period of 1987-2000 using copula functions. To determine the appropriate choice of the joint default process, we propose a new metric. This metric accounts for different aspects of default correlation, namely (i) level, (ii) asymmetry and (iii) tail-dependence and extreme behavior. Our model, based on estimating a joint system of over 600 issuers, is designed to replicate the empirical joint distribution of defaults. A comparison of a jump model and a regime-switching model shows that the latter provides a better representation of the properties of correlated default. We also find that the skewed double-exponential distribution is the best choice for the marginal distribution of each issuer's hazard rate process, and combines well with the normal, Gumbel, Clayton and student's t copulas in the joint dependence relationship amongst issuers. As a complement to the methodological innovation, we show that (a) appropriate choices of marginal distributions and copulas are essential in modeling correlated default, (b) accounting for regimes is an important aspect of joint specifications of default risk, and (c) misspecification of credit portfolio risk can occur easily if joint distributions are inappropriately chosen. The empirical evidence suggests that improvements are indeed possible over the standard Gaussian copula used in practice.
Author: Sanjiv Ranjan Das Publisher: ISBN: Category : Languages : en Pages : 37
Book Description
Modeling correlated default risk is a new phenomenon currently sweeping through the credit markets. In this paper, we develop a methodology to model, simulate and assess the joint default process of hundreds of issuers. Our study is based on a data set of default probabilities supplied by Moody's Risk Management Services. We undertake an empirical examination of the joint stochastic process of default risk over the period of 1987-2000 using copula functions. To determine the appropriate choice of the joint default process, we propose a new metric. This metric accounts for different aspects of default correlation, namely (i) level, (ii) asymmetry and (iii) tail-dependence and extreme behavior. Our model, based on estimating a joint system of over 600 issuers, is designed to replicate the empirical joint distribution of defaults. A comparison of a jump model and a regime-switching model shows that the latter provides a better representation of the properties of correlated default. We also find that the skewed double-exponential distribution is the best choice for the marginal distribution of each issuer's hazard rate process, and combines well with the normal, Gumbel, Clayton and student's t copulas in the joint dependence relationship amongst issuers. As a complement to the methodological innovation, we show that (a) appropriate choices of marginal distributions and copulas are essential in modeling correlated default, (b) accounting for regimes is an important aspect of joint specifications of default risk, and (c) misspecification of credit portfolio risk can occur easily if joint distributions are inappropriately chosen. The empirical evidence suggests that improvements are indeed possible over the standard Gaussian copula used in practice.
Author: Xiaowei Ding Publisher: Stanford University ISBN: Category : Languages : en Pages : 120
Book Description
Credit risk pervades all nancial transactions. The credit crisis has indicated the need for quantitative models for valuation, hedging, rating, risk management and regulatory monitoring of credit risk. A credit investor such as a bank granting loans to rms or an asset manager buying corporate bonds is exposed to correlated default risk. A portfolio credit derivative is a nancial security that allows the investor to transfer this risk to the credit market. In the rst part of this thesis, we study the valuation and risk analysis of portfolio derivatives. To capture the complex economic phenomena that drive the pricing of these securities, we introduce a time-changed birth process as a probabilistic model of correlated event timing. The self-exciting property of a time-changed birth process captures the feedback from events that is often observed in credit markets. The stochastic variation of arrival rates between events captures the exposure of rms to common economic risk factors. We derive a closed-form expression for the distribution of a time-changed birth process, and develop analytically tractable pricing relations for a range of portfolio derivatives valuation problems. We illustrate our results by calibrating a tranche forward and option pricer to market rates of index and tranche swaps. A loss point process model such as a time-changed birth process is speci ed without reference to the portfolio constituents. It is silent about the portfolio constituent risks, and cannot be used to address applications that are based on the relationship between portfolio and component risks, for example constituent risk hedging. The second part of this thesis develops a method that extends the reach of these models to the constituents. We use random thinning to decompose the portfolio intensity into the sum of the constituent intensities. We show that a thinning process, which allocates the portfolio intensity to constituents, uniquely exists and is a probabilistic model for the next-to-default. We derive a formula for the constituent default probability in terms of the thinning process and the portfolio intensity, and develop a semi-analytical transform approach to evaluate it. The formula leads to a calibration scheme for the thinning processes, and an estimation scheme for constituent hedge sensitivities. An empirical analysis for September 2008 shows that the constituent hedges generated by our method outperform the hedges prescribed by the Gaussian copula model, which is widely used in practice.
Author: Alexander Lipton Publisher: World Scientific ISBN: 9812709495 Category : Business & Economics Languages : en Pages : 178
Book Description
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.
Author: Youssef Elouerkhaoui Publisher: Springer ISBN: 3319609734 Category : Business & Economics Languages : en Pages : 466
Book Description
This book provides an advanced guide to correlation modelling for credit portfolios, providing both theoretical underpinnings and practical implementation guidance. The book picks up where pre-crisis credit books left off, offering guidance for quants on the latest tools and techniques for credit portfolio modelling in the presence of CVA (Credit Value Adjustments). Written at an advanced level, it assumes that readers are familiar with the fundamentals of credit modelling covered, for example, in the market leading books by Schonbucher (2003) and O’Kane (2008). Coverage will include the latest default correlation approaches; correlation modelling in the ‘Marshall-Olkin’ contagion framework, in the context of CVA; numerical implementation; and pricing, calibration and risk challenges. The explosive growth of credit derivatives markets in the early-to-mid 000’s was bought to a close by the 2007 financial crisis, where these instruments were held largely to blame for the economic downturn. However, in the wake of increased regulation across all financial instruments and the challenge of buying and selling bonds in large amounts, credit derivatives have once again been found to be the answer and the market has grown significantly. Written by a practitioner for practitioners, this book will also interest researchers in mathematical finance who want to understand how things happen and work ‘on the floor’. Building the reader’s knowledge from the ground up, and with numerous real life examples used throughout, this book will prove a popular reference for anyone with a mathematical mind interested credit markets.
Author: Niklas Wagner Publisher: CRC Press ISBN: 1584889950 Category : Business & Economics Languages : en Pages : 600
Book Description
Featuring contributions from leading international academics and practitioners, Credit Risk: Models, Derivatives, and Management illustrates how a risk management system can be implemented through an understanding of portfolio credit risks, a set of suitable models, and the derivation of reliable empirical results. Divided into six sectio
Author: Sergio M. Focardi Publisher: John Wiley & Sons ISBN: 0471674230 Category : Business & Economics Languages : en Pages : 802
Book Description
the mathematics of financial modeling & investment management The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.
Author: Yi Tang Publisher: World Scientific ISBN: 9812706658 Category : Business & Economics Languages : en Pages : 523
Book Description
This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authorsOCO own research and practice. While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, and foreign exchange markets. This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view of financial engineers or practitioners, and, as such, it puts more emphasis on the practical applications of financial mathematics in the real market than the mathematics itself with precise (and tedious) technical conditions. It attempts to combine economic insights with mathematics and modeling so as to help the reader develop intuitions. In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies, which are relatively recent developments and are of increasing importance. It also discusses various trading structuring strategies and touches upon some popular credit/IR/FX hybrid products, such as PRDC, TARN, Snowballs, Snowbears, CCDS, credit extinguishers."
Author: Sanjiv Ranjan Das
Author: Sanjiv Ranjan Das
Author: Xiaowei Ding
Author: Alexander Lipton
Author: Ismail Onur Filiz
Author: Youssef Elouerkhaoui
Author: Niklas Wagner
Author: Sergio M. Focardi
Author: Kasper Mundbjerg Eriksen
Author: Darrell Duffie
Author: Yi Tang