From the late 1990s, the spectacular growth of a secondary market for credit through derivatives has been matched by the emergence of mathematical modelling analysing the credit risk embedded in these contracts. This book aims to provide a broad and deep overview of this modelling, covering statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modelling, and securitisation. Both reduced-form and firm-value models for the default of single entities are considered in detail, with extensive discussion of both their theoretical underpinnings and practical usage in pricing and risk. For multiple entity modelling, the now notorious Gaussian copula is discussed with analysis of its shortcomings, as well as a wide range of alternative approaches including multivariate extensions to both firm-value and reduced form models, and continuous-time Markov chains. One important case of multiple entities modelling - counterparty risk in credit derivatives - is further explored in two dedicated chapters. Alternative non-Gaussian approaches to modelling are also discussed, including extreme-value theory and saddle-point approximations to deal with tail risk. Finally, the recent growth in securitisation is covered, including house price modelling and pricing models for asset-backed CDOs. The current credit crisis has brought modelling of the previously arcane credit markets into the public arena. Lipton and Rennie with their excellent team of contributors, provide a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. Though technical in nature, the pros and cons of various approaches attempt to provide a balanced view of the role that mathematical modelling plays in the modern credit markets. This book will appeal to students and researchers in statistics, economics, and finance, as well as practitioners, credit traders, and quantitative analysts
A comprehensive resource providing extensive coverage of the state of the art in credit secruritisations, derivatives, and risk management Credit Securitisations and Derivatives is a one-stop resource presenting the very latest thinking and developments in the field of credit risk. Written by leading thinkers from academia, the industry, and the regulatory environment, the book tackles areas such as business cycles; correlation modelling and interactions between financial markets, institutions, and instruments in relation to securitisations and credit derivatives; credit portfolio risk; credit portfolio risk tranching; credit ratings for securitisations; counterparty credit risk and clearing of derivatives contracts and liquidity risk. As well as a thorough analysis of the existing models used in the industry, the book will also draw on real life cases to illustrate model performance under different parameters and the impact that using the wrong risk measures can have.
Since the development of the Black-Scholes model, research on equity derivatives has evolved rapidly to the point where it is now difficult to cut through the myriad of literature to find relevant material. Written by a quant with many years of experience in the field this book provides an up-to-date account of equity and equity-hybrid (equity-rates, equity-credit, equity-foreign exchange) derivatives modeling from a practitioner's perspective. The content reflects the requirements of practitioners in financial institutions: Quants will find a survey of state-of-the-art models and guidance on how to efficiently implement them with regards to market data representation, calibration, and sensitivity computation. Traders and structurers will learn about structured products, selection of the most appropriate models, as well as efficient hedging methods while risk managers will better understand market, credit, and model risk and find valuable information on advanced correlation concepts. Equity Derivatives and Hybrids provides exhaustive coverage of both market standard and new approaches, including: -Empirical properties of stock returns including autocorrelation and jumps -Dividend discount models -Non-Markovian and discrete-time volatility processes -Correlation skew modeling via copula as well as local and stochastic correlation factors -Hybrid modeling covering local and stochastic processes for interest rate, hazard rate, and volatility as well as closed form solutions -Credit, debt, and funding valuation adjustment (CVA, DVA, FVA) -Monte Carlo techniques for sensitivities including algorithmic differentiation, path recycling, as well as multilevel. Written in a highly accessible manner with examples, applications, research, and ideas throughout, this book provides a valuable resource for quantitative-minded practitioners and researchers.
This book combines academic research and practical expertise on alternative assets and trading strategies in a unique way. The asset classes that are discussed include : credit risk, cross-asset derivatives, energy, private equity, freight agreements, alternative real assets (ARA), and socially responsible investments (SRI). The coverage on trading and investment strategies are directed at portfolio insurance, especially constant proportion portfolio insurance (CPPI) and constant proportion debt obligation (CPDO) strategies, robust portfolio optimization, and hedging strategies for exotic options.
The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lvy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
The first decade of the 21st Century has been disastrous for financial institutions, derivatives and risk management. Counterparty credit risk has become the key element of financial risk management, highlighted by the bankruptcy of the investment bank Lehman Brothers and failure of other high profile institutions such as Bear Sterns, AIG, Fannie Mae and Freddie Mac. The sudden realisation of extensive counterparty risks has severely compromised the health of global financial markets. Counterparty risk is now a key problem for all financial institutions. This book explains the emergence of counterparty risk during the recent credit crisis. The quantification of firm-wide credit exposure for trading desks and businesses is discussed alongside risk mitigation methods such as netting and collateral management (margining). Banks and other financial institutions have been recently developing their capabilities for pricing counterparty risk and these elements are considered in detail via a characterisation of credit value adjustment (CVA). The implications of an institution valuing their own default via debt value adjustment (DVA) are also considered at length. Hedging aspects, together with the associated instruments such as credit defaults swaps (CDSs) and contingent CDS (CCDS) are described in full. A key feature of the credit crisis has been the realisation of wrong-way risks illustrated by the failure of monoline insurance companies. Wrong-way counterparty risks are addressed in detail in relation to interest rate, foreign exchange, commodity and, in particular, credit derivative products. Portfolio counterparty risk is covered, together with the regulatory aspects as defined by the Basel II capital requirements. The management of counterparty risk within an institution is also discussed in detail. Finally, the design and benefits of central clearing, a recent development to attempt to control the rapid growth of counterparty risk, is considered. This book is unique in being practically focused but also covering the more technical aspects. It is an invaluable complete reference guide for any market practitioner with any responsibility or interest within the area of counterparty credit risk.
The global fixed income market is an enormous financial market whose value by far exceeds that of the public stock markets. The interbank market consists of interest rate derivatives, whose primary purpose is to manage interest rate risk. The credit market primarily consists of the bond market, which links investors to companies, institutions, and governments with borrowing needs. This dissertation takes an optimization perspective upon modeling both these areas of the fixed-income market. Legislators on the national markets require financial actors to value their financial assets in accordance with market prices. Thus, prices of many assets, which are not publicly traded, must be determined mathematically. The financial quantities needed for pricing are not directly observable but must be measured through solving inverse optimization problems. These measurements are based on the available market prices, which are observed with various degrees of measurement noise. For the interbank market, the relevant financial quantities consist of term structures of interest rates, which are curves displaying the market rates for different maturities. For the bond market, credit risk is an additional factor that can be modeled through default intensity curves and term structures of recovery rates in case of default. By formulating suitable optimization models, the different underlying financial quantities can be measured in accordance with observable market prices, while conditions for economic realism are imposed. Measuring and managing risk is closely connected to the measurement of the underlying financial quantities. Through a data-driven method, we can show that six systematic risk factors can be used to explain almost all variance in the interest rate curves. By modeling the dynamics of these six risk factors, possible outcomes can be simulated in the form of term structure scenarios. For short-term simulation horizons, this results in a representation of the portfolio value distribution that is consistent with the realized outcomes from historically observed term structures. This enables more accurate measurements of interest rate risk, where our proposed method exhibits both lower risk and lower pricing errors compared to traditional models. We propose a method for decomposing changes in portfolio values for an arbitrary portfolio into the risk factors that affect the value of each instrument. By demonstrating the method for the six systematic risk factors identified for the interbank market, we show that almost all changes in portfolio value and portfolio variance can be attributed to these risk factors. Additional risk factors and approximation errors are gathered into two terms, which can be studied to ensure the quality of the performance attribution, and possibly improve it. To eliminate undesired risk within trading books, banks use hedging. Traditional methods do not take transaction costs into account. We, therefore, propose a method for managing the risks in the interbank market through a stochastic optimization model that considers transaction costs. This method is based on a scenario approximation of the optimization problem where the six systematic risk factors are simulated, and the portfolio variance is weighted against the transaction costs. This results in a method that is preferred over the traditional methods for all risk-averse investors. For the credit market, we use data from the bond market in combination with the interbank market to make accurate measurements of the financial quantities. We address the notoriously difficult problem of separating default risk from recovery risk. In addition to the previous identified six systematic risk factors for risk-free interests, we identify four risk factors that explain almost all variance in default intensities, while a single risk factor seems sufficient to model the recovery risk. Overall, this is a higher number of risk factors than is usually found in the literature. Through a simple model, we can measure the variance in bond prices in terms of these systematic risk factors, and through performance attribution, we relate these values to the empirically realized variances from the quoted bond prices. De globala ränte- och kreditmarknaderna är enorma finansiella marknader vars sammanlagda värden vida överstiger de publika aktiemarknadernas. Räntemarknaden består av räntederivat vars främsta användningsområde är hantering av ränterisker. Kreditmarknaden utgörs i första hand av obligationsmarknaden som syftar till att förmedla pengar från investerare till företag, institutioner och stater med upplåningsbehov. Denna avhandling fokuserar på att utifrån ett optimeringsperspektiv modellera både ränte- och obligationsmarknaden. Lagstiftarna på de nationella marknaderna kräver att de finansiella aktörerna värderar sina finansiella tillgångar i enlighet med marknadspriser. Därmed måste priserna på många instrument, som inte handlas publikt, beräknas matematiskt. De finansiella storheter som krävs för denna prissättning är inte direkt observerbara, utan måste mätas genom att lösa inversa optimeringsproblem. Dessa mätningar görs utifrån tillgängliga marknadspriser, som observeras med varierande grad av mätbrus. För räntemarknaden utgörs de relevanta finansiella storheterna av räntekurvor som åskådliggör marknadsräntorna för olika löptider. För obligationsmarknaden utgör kreditrisken en ytterligare faktor som modelleras via fallissemangsintensitetskurvor och kurvor kopplade till förväntat återvunnet kapital vid eventuellt fallissemang. Genom att formulera lämpliga optimeringsmodeller kan de olika underliggande finansiella storheterna mätas i enlighet med observerbara marknadspriser samtidigt som ekonomisk realism eftersträvas. Mätning och hantering av risker är nära kopplat till mätningen av de underliggande finansiella storheterna. Genom en datadriven metod kan vi visa att sex systematiska riskfaktorer kan användas för att förklara nästan all varians i räntekurvorna. Genom att modellera dynamiken i dessa sex riskfaktorer kan tänkbara utfall för räntekurvor simuleras. För kortsiktiga simuleringshorisonter resulterar detta i en representation av fördelningen av portföljvärden som väl överensstämmer med de realiserade utfallen från historiskt observerade räntekurvor. Detta möjliggör noggrannare mätningar av ränterisk där vår föreslagna metod uppvisar såväl lägre risk som mindre prissättningsfel jämfört med traditionella modeller. Vi föreslår en metod för att dekomponera portföljutvecklingen för en godtycklig portfölj till de riskfaktorer som påverkar värdet för respektive instrument. Genom att demonstrera metoden för de sex systematiska riskfaktorerna som identifierats för räntemarknaden visar vi att nästan all portföljutveckling och portföljvarians kan härledas till dessa riskfaktorer. Övriga riskfaktorer och approximationsfel samlas i två termer, vilka kan användas för att säkerställa och eventuellt förbättra kvaliteten i prestationshärledningen. För att eliminera oönskad risk i sina tradingböcker använder banker sig av hedging. Traditionella metoder tar ingen hänsyn till transaktionskostnader. Vi föreslår därför en metod för att hantera riskerna på räntemarknaden genom en stokastisk optimeringsmodell som också tar hänsyn till transaktionskostnader. Denna metod bygger på en scenarioapproximation av optimeringsproblemet där de sex systematiska riskfaktorerna simuleras och portföljvariansen vägs mot transaktionskostnaderna. Detta resulterar i en metod som, för alla riskaverta investerare, är att föredra framför de traditionella metoderna. På kreditmarknaden använder vi data från obligationsmarknaden i kombination räntemarknaden för att göra noggranna mätningar av de finansiella storheterna. Vi angriper det erkänt svåra problemet att separera fallissemangsrisk från återvinningsrisk. Förutom de tidigare sex systematiska riskfaktorerna för riskfri ränta, identifierar vi fyra riskfaktorer som förklarar nästan all varians i fallissemangsintensiteter, medan en enda riskfaktor tycks räcka för att modellera återvinningsrisken. Sammanlagt är detta ett större antal riskfaktorer än vad som brukar användas i litteraturen. Via en enkel modell kan vi mäta variansen i obligationspriser i termer av dessa systematiska riskfaktorer och genom prestationshärledningen relatera dessa värden till de empiriskt realiserade varianserna från kvoterade obligationspriser.
Credit Default Swaps: A Survey is the most comprehensive review of all major research domains involving credit default swaps (CDS). CDS have been growing in importance in the global financial markets. However, their role has been hotly debated, in industry and academia, particularly since the credit crisis of 2007-2009. The authors review the extant literature on CDS that has accumulated over the past two decades and divide the survey into seven topics after providing a broad overview in the introduction. The second section traces the historical development of CDS markets and provides an introduction to CDS contract definitions and conventions. The third section discusses the pricing of CDS, from the perspective of no-arbitrage principles, structural, and reduced-form credit risk models. It also summarizes the literature on the determinants of CDS spreads, with a focus on the role of fundamental credit risk factors, liquidity and counterparty risk. The fourth section discusses how the development of the CDS market has affected the characteristics of the bond and equity markets, with an emphasis on market efficiency, price discovery, information flow, and liquidity. Attention is also paid to the CDS-bond basis, the wedge between the pricing of the CDS and its reference bond, and the mispricing between the CDS and the equity market. The fifth section examines the effect of CDS trading on firms' credit and bankruptcy risk, and how it affects corporate financial policy, including bond issuance, capital structure, liquidity management, and corporate governance. The sixth section analyzes how CDS impact the economic incentives of financial intermediaries. The seventh section reviews the growing literature on sovereign CDS and highlights the major differences between the sovereign and corporate CDS markets. The eighth section discusses CDS indices, especially the role of synthetic CDS index products backed by residential mortgage-backed securities during the financial crisis. The authors close with our suggestions for promising future research directions on CDS contracts and markets.
