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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Quantitative Portfolio Management Part 1 : Capital Structure Arbitrage Pierre GARREAU Florida State University 17 septembre 2009 P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Press Review Punch Line Mise en Bouche Definitions Press Review Volkswagen, Europe’s biggest carmarker, and Gas natural, Spain’s largest natural gaz provider, are among companies for which the increase in Credit Protection costs has been disproportionate relative to the move in their equity prices and stock volatility. ABN Amro Holding NV, 14 Février, 2008 Credit Default Swaps for Wolfsburg have increased 155% this year. The stock is down 4% in 2008 and the implied volatility has decreased to 26% from 32% at the start of the year. Bloomberg, 22 Février, 2008 Telecom Italia’s stock price and Credit Default Swap seem to be increasingly correlated, suggesting arbitrage opportunities. Exane BNP Paribas - Equity Research, 31 Mars, 2008 P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Press Review Punch Line Mise en Bouche Definitions Fig.: 5Y CDS spread on Volkswagen SNR (light blue) - Equity (light purple) - 6 months put implied volality (dark blue) P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Press Review Punch Line Mise en Bouche Definitions Capital Structure Arbitrage : Strategy that exploits the discrepancies of prices between derivative products based on the same Capital Structure P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Press Review Punch Line Mise en Bouche Definitions Mise en Bouche Price Difference - Reproduce the behavior of CDS Spread based on information available in the Equity Market Capital Structure - Clarify the Theory of Structurarl Models Strategy - Implement a trading algorithm based on Capital Structure Arbitrage relying on Equity/CDS positions P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Press Review Punch Line Mise en Bouche Definitions Credit Risk The value of the contract at par is so that the two legs equate each other m ( t , T ) = ( 1 - R ) 1 - R T t e - r ( T - t ) d P ( u ) R T t e - r ( T - u ) P ( u ) d u P. Garreau Capital Structure Arbitrage
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Introduction Structural Models CreditGrades Calibration Capital Structure Arbitrage Critiques and Extension Ouverture Merton’s Framework « Passage »Time and Moving Barrier Firm’s Valuation (Modigliani-Miller) Assets Liabilities Value of the Firm V t Equity S t Debt B t The value of the Firm at Maturity is Debt B T , prorated if V T < B Debt B + Equity S T if V T B P. Garreau Capital Structure Arbitrage
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