
Contents
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1 Introduction 1 Introduction
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2 The conventional term structure Measures 2 The conventional term structure Measures
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2.1 The strippable cash flow valuation methodology 2.1 The strippable cash flow valuation methodology
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2.2 The conventional bond yield and spread measures 2.2 The conventional bond yield and spread measures
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2.2.1 Risk‐free bonds 2.2.1 Risk‐free bonds
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2.2.2 Bullet bonds: yield spread 2.2.2 Bullet bonds: yield spread
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2.2.3 Bullet bonds: Z‐spread 2.2.3 Bullet bonds: Z‐spread
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2.2.4 Callable/puttable bonds: option‐adjusted spread (OAS) 2.2.4 Callable/puttable bonds: option‐adjusted spread (OAS)
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2.2.5 Floating rate notes: discount margin 2.2.5 Floating rate notes: discount margin
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3 The phenomenology of credit pricing 3 The phenomenology of credit pricing
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3.1 Credit bond cash flows reconsidered 3.1 Credit bond cash flows reconsidered
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3.2 The implications of risky cash flows 3.2 The implications of risky cash flows
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4 The survival‐based valuation of credit‐risky securities 4 The survival‐based valuation of credit‐risky securities
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4.1 The single‐name credit market instruments 4.1 The single‐name credit market instruments
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4.2 The recovery assumptions in the reduced‐form framework 4.2 The recovery assumptions in the reduced‐form framework
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4.3 Pricing of credit bonds 4.3 Pricing of credit bonds
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4.4 Pricing of CDS 4.4 Pricing of CDS
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4.5 The credit triangle and default rate calibration 4.5 The credit triangle and default rate calibration
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5 Empirical estimation of survival probabilities 5 Empirical estimation of survival probabilities
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6 Issuer and sector credit term structures 6 Issuer and sector credit term structures
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6.1 Survival and default probability term structures 6.1 Survival and default probability term structures
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6.2 Hazard rate and ZZ‐spread term structures 6.2 Hazard rate and ZZ‐spread term structures
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6.3 Par coupon and P‐spread term structures 6.3 Par coupon and P‐spread term structures
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6.4 Constant coupon price (CCP) term structure 6.4 Constant coupon price (CCP) term structure
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6.5 Bond‐implied CDS (BCDS) term structure 6.5 Bond‐implied CDS (BCDS) term structure
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6.6 Forward spreads and forward trades 6.6 Forward spreads and forward trades
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7 Bond‐specific valuation measures 7 Bond‐specific valuation measures
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7.1 Fitted price and P‐spread 7.1 Fitted price and P‐spread
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7.2 Default‐adjusted spread and excess spread 7.2 Default‐adjusted spread and excess spread
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8 The CDS‐Bond basis 8 The CDS‐Bond basis
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8.1 The CDS‐Bond complementarity 8.1 The CDS‐Bond complementarity
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8.2 Static hedging of credit bonds with CDS 8.2 Static hedging of credit bonds with CDS
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8.3 Consistent measures for CDS‐Bond basis 8.3 Consistent measures for CDS‐Bond basis
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8.4 The coarse‐grained hedging and approximate basis 8.4 The coarse‐grained hedging and approximate basis
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9 Conclusions 9 Conclusions
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Appendices Appendices
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A Exponential splines A Exponential splines
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B Continuous time approximation for credit bond and CDS pricing B Continuous time approximation for credit bond and CDS pricing
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References References
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4 A Guide to Modelling credit term Structures
Get accessAlexander Lipton is a Managing Director and Co-Head of the Global Quantitative Group at Bank of America Merrill Lynch, and Visiting Professor of Mathematics at Imperial College. Prior to his current role, he was Managing Director and Head of Capital Structure Quantitative Research at Citadel Investment Group in Chicago. He has also worked at Credit Suisse, Deutsche Bank, and Bankers Trust. Previously, he was a Full Professor of Mathematics at the University of Illinois, Chicago, and Consultant at Los Alamos National Laboratory. He received his undergraduate and graduate degrees from Moscow State University. Professor Lipton is author of two books and editor of three. He has published numerous research papers on hydrodynamics, magnetohydrodynamics, astrophysics, and financial engineering. He has delivered many invited lectures at leading universities and major conferences worldwide.
Andrew Rennie has spent sixteen years in finance, specialising in derivatives pricing and risk management. He has worked at UBS, Rabobank International, and Merrill Lynch, where he managed all quantitative and modelling activity in derivatives across fixed income, credit, foreign exchange, commodities, and equities globally. He retired from Merrill Lynch in 2009 to advise on pricing and risk issues to governments, regulators, banks, and hedge funds. He graduated with a First in Mathematics from Cambridge University and published papers in Mathematical Chemistry on the properties of one-dimensional inclusion compounds. He co-authored a textbook on derivative pricing- Financial Calculus- and has also co-edited Credit Correlation - Life after Copulas.
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Published:18 September 2012
Cite
Abstract
This article examines the conventional bond pricing methodology and shows that it does not adequately reflect the nature of the credit risk faced by investors. In particular, it demonstrates that the strippable discounted cash flows valuation assumption, which is normally taken for granted by most analysts, leads to biased estimates of relative value for credit bonds. The article introduces a consistent survival-based valuation methodology that is free of biases, albeit at a price of abandoning the strippable discounted cash flows valuation assumption, and also develops a robust estimation methodology for survival probability term structures using the exponential splines approximation. This methodology is implemented and tested in a wide variety of market conditions, and across a large set of sectors and issuers, from the highest credit quality to highly distressed ones. It concludes that the adoption of the survival-based methodologies advocated in this article by market participants will lead to an increase in the efficiency of the credit markets, just as the adoption of better pre-payment models led to efficiency in the mortgage-based securities markets twenty years ago.
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