A Spot Stochastic Recovery Extension of the Gaussian Copula

The market evolution since the end of 2007 has been characterized by an increase of systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels. This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk.stochastic recovery, CDO, correlation smile, base correlation, copula, factor model, default risk

CVA, Wrong Way Risk, Hedging and Bermudan Swaption

“Roughly two-thirds of credit counterparty losses were due to credit valuation adjustment losses and only one-third were due to actual defaults” according to the Basel Committee on Banking Supervision, highlighting the importance of counterparty credit risk management to the derivatives contracts. Today, managing counterparty credit risk has become an integrated part of many derivative trading desks’ day-to-day activities and the need of accurate pricing, efficient hedging strategies and practical proxies has become critical. As a result, banks have sharpened their CVA pricing and modeling infrastructure and most have a dedicated trading desk dynamically hedging their CVA. However, if pricing techniques have become standard over the past few years, the expected positive exposure (EPE) modeling is usually not taking into account the embedded correlation between the counterparty and underlying market movements. This correlation known as wrong way risk can substantially affect the price and the related hedging strategy and is the main focus of this article

A Spot Stochastic Recovery Extension of the Gaussian Copula

The market evolution since the end of 2007 has been characterized by an increase of systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels. This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk

CVA, Wrong Way Risk, Hedging and Bermudan Swaption

“Roughly two-thirds of credit counterparty losses were due to credit valuation adjustment losses and only one-third were due to actual defaults” according to the Basel Committee on Banking Supervision, highlighting the importance of counterparty credit risk management to the derivatives contracts. Today, managing counterparty credit risk has become an integrated part of many derivative trading desks’ day-to-day activities and the need of accurate pricing, efficient hedging strategies and practical proxies has become critical. As a result, banks have sharpened their CVA pricing and modeling infrastructure and most have a dedicated trading desk dynamically hedging their CVA. However, if pricing techniques have become standard over the past few years, the expected positive exposure (EPE) modeling is usually not taking into account the embedded correlation between the counterparty and underlying market movements. This correlation known as wrong way risk can substantially affect the price and the related hedging strategy and is the main focus of this article