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Credit Risk
  • Recent Issues in the Pricing of Collateralized Derivatives Contracts presentation , Jean-Paul Laurent (2014)
  • Collateral and Credit Issues in Derivatives Pricing Regulatory changes are increasing the importance of collateral agreements and credit issues in over-the-counter derivatives transactions. This paper considers the nature of derivatives collateral agreements and examines the impact of collateral agreements, two-sided credit risk, funding costs, liquidity, and bid-offer spreads on the valuation of derivatives portfolios. , John Hull and Alan White (2014)
  • Optimal Posting of Sticky Collateral We study optimal strategies for posting collateral for OTC derivatives under Credit Support Annexes (CSAs) where "substitution rights'' either do not exist or are hard to enforce. We present a simplified model which we are able to solve approximately in an efficient manner. Additionally we show that the optimal posting strategy is defined by the relation between suitably-defined term, rather than instantaneous, collateral rates, as would be the case in "full substitution'' situations that have been studied in the literature so far. , Vladimir Piterbarg (2013)
  • CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed on simple single asset classes to simple derivatives embedding the new or previously neglected types of complex and interconnected nonlinear risks we address here. This dialogue is the continuation of the "Counterparty Risk, Collateral and Funding FAQ" by Brigo (2011). In this dialogue we focus more on funding costs for the hedging strategy of a portfolio of trades, on the non-linearities emerging from assuming borrowing and lending rates to be different, on the resulting aggregation-dependent valuation process and its operational challenges, on the implications of the onset of central clearing, on the macro and micro effects on valuation and risk of the onset of CCPs, on initial and variation margins impact on valuation, and on multiple discount curves. Through questions and answers (Q&A) between a senior expert and a junior colleague, and by referring to the growing body of literature on the subject, we present a unified view of valuation (and risk) that takes all such aspects into account. , Damiano Brigo, Andrea Pallavicini (2013)
  • CVA AND WRONG WAY RISK This paper proposes a simple model for incorporating wrong-way and right-way risk into CVA (credit value adjustment) calculations. These are the calculations, involving Monte Carlo simulation, made by a dealer to determine the reduction in the value of its derivatives portfolio because of the possibility of a counterparty default. The model assumes a relationship between the hazard rate of the counterparty and variables whose values can be generated as part of the Monte Carlo simulation. Numerical results for portfolios of 25 instruments dependent on five underlying market variables are presented. The paper finds that wrong-way and right-way risk have a significant effect on the Greek letters of CVA as well as on CVA itself. It also finds that the percentage effect depends on the collateral arrangements , John Hull and Alan White (2012)
  • An overview of the valuation of collateralized derivative contracts We consider the valuation of collateralized derivative contracts such as interest rate swaps, forward FX contracts or term repos. First, we provide a precise framework regarding collateralization, under which computations are made easy. We allow for posting securities or cash in different currencies. In the latter case, we focus on using overnight index rates on the interbank market, in line with LCH.Clearnet framework. We provide an intuitive way to derive the basic discounting results, keeping in line with the most standard theoretical and market views. Under perfect collateralization, pricing rules for collateralized trades remain linear, thus the use of (multiple) discount curves. We then show how to deal with partial collateralization, involving haircuts, asymmetric CSA, counterparty risk and funding costs as an extension of the perfect collateralization case. We therefore intend to provide a unified view. Mathematical or legal details are not dealt with and we privilege financial intuition and easy to grasp concepts and tools. , Jean-Paul LAURENT , Philippe AMZELEK and Joe BONNAUD (2012)
  • Collateral,Funding and Discounting presentation , Vladimir V. Piterbarg (2012)
  • Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral modeling, Gap Risk, Re-hypothecation, Wrong Way Risk, Basel III, inclusion of Funding costs, First to Default risk, Contingent Credit Default Swaps (CCDS) and CVA restructuring possibilities through margin lending. The dialogue is in the form of a Q&A between a CVA expert and a newly hired colleague , Damiano Brigo (2011)
  • Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA?s) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in Brigo and Capponi (2008), including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work. , D.Brigo, A.Pallavicini, V.Papatheodorou (2009)
  • The Risk of Tranches Created from Residential Mortgages This paper examines the risk in the tranches of ABSs and ABS CDOs that were created from residential mortgages between 2000 and 2007. Using the criteria of the rating agencies, it tests how wide the AAA tranches can be under different assumptions about the correlation model and recovery rates. It concludes that the AAA ratings assigned to the senior tranches of ABSs were not unreasonable. However, the AAA ratings assigned to tranches of Mezz ABS CDOs cannot be justified. The risk of a Mezz ABS CDO tranche depends critically on the correlation between mortgage pools as well as on the correlation model and the thickness of the underlying BBB tranches. The BBB tranches of ABSs cannot be considered equivalent to BBB bonds for the purposes of subsequent securitizations. , J.Hull, A.White (2009)
  • Burnout from pools to loans: Modeling refinancing prepayments as a self-selection process In this paper we present compelling evidence from a detailed analysis of historical prepayment data to demonstrate that a mortgage cohort remem- bers the level of the previous mortgage rate troughs experienced by the co- hort. This is a general property, observed ubiquitously, that inescapably leads to refinancing models with a continuous distribution of refinancing incentive thresholds (elbows). We present such a new refinancing model, derived from the rst principle, based on a single assumption that each loan has an in- centive threshold above which its borrower will refinance. In this model, the refinancing prepayment of a cohort is a dynamic self-selection process that evolves by itself according to the encountered mortgage rate environment with the cohort concurrently acquiring its memory along the way. , Junwu Gan (2009)
  • Up And Down Credit Risk , T.Bielicki, S.Crepey, M.Jeanblanc (2008)
  • Mortality Fluctuations Modelling with a Shared Frailty Approach , J.P.Laurent, S.Fulla (2008)
  • The Credit Crunch of 2007: What Went Wrong? Why? What Lessons Can Be Learned? , J.C.Hull (2008)
  • Credit Risk Models , J.P.Laurent (2008)
  • Credit Risk Models , M.Jeanblanc, T.R.Bielecki, M.Rutkowski (2007)
  • Reduced form modelling for credit risk , M.Jeanblanc, Y.Le Cam (2007)
  • Credit Risk , M.Jeanblanc (2006)
  • Merton?s Model, Credit Risk, and Volatility Skews , J.Hull, A.White, I.Nelken (2004)
  • A Comparative Analysis of Current Credit Risk Models , M.Crouhy, D.Galai, R.Mark (2000)
  • Pricing Credit Risk Derivatives , P. J. Sch?nbucher (1998)

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