CONFERENCE ON CREDIT RISK | Chicago, October 19-20, 2007
PROGRAM
The sequence of talks within each day is subject to change, but we do not expect to switch a talk from one day to the other day. Return to main conference page.
| Time | Speaker | Title (click for abstract) |
|---|---|---|
| 8:30am | Breakfast | |
| 9:00am | Michael Gordy | The Bank as Grim Reaper: Debt Composition and Recoveries on Defaulted Debt |
| 9:50am | Sanjiv Das | Implied Recovery |
| 10:40am | Morning Break | |
| 11:10am | Donald van Deventer | The Variation in Implications of Alternative CDO and Credit Portfolio Modeling Techniques |
| 12:00pm | Lunch | |
| 1:10pm | Terry Benzschawel | Corporate Loan and LCDS Pricing and Relative Value |
| 2:00pm | Bjorn Flesaker | Replication Based Pricing of Default Contingent Claims |
| 2:50pm | Afternoon Break | |
| 3:20pm | Vadim Linetsky | Time-Changed Markov Processes in Credit-Equity Modeling |
| 4:10pm | Monique Jeanblanc | Pricing and Trading Credit Default Swaps in a Multidefault Setting |
| 5:00pm | Reception | |
| 6:00pm | Dinner |
| Time | Speaker | Title (click for abstract) |
|---|---|---|
| 8:30am | Breakfast | |
| 9:00am | Rama Cont | Recovering Credit Portfolio Loss Rates from CDO Tranches |
| 9:50am | Ruediger Frey | Dynamic Hedging of Synthetic CDO Tranches with Spread and Contagion Risk |
| 10:40am | Morning Break | |
| 11:10am | John Hull | Dynamic Models of Portfolio Credit Risk: A Simplified Approach |
| 12:00pm | Lunch | |
| 1:10pm | Kay Giesecke | Pricing, Hedging and Calibrating Credit from the Top Down |
| 2:00pm | Igor Halperin | Credit Top Down Models: Climbing Down from the Top |
| 2:50pm | Afternoon Break | |
| 3:20pm | Damiano Brigo | Default Correlation, Cluster Dynamics and Single Names: The GPCL Dynamical Loss Model |
| 4:10pm | Practitioner Panel Discussion | What Are the Modeling Challenges Facing the Credit Markets? |
| 5:00pm | Conference ends |
PRACTITIONER PANEL DISCUSSION
- What Are the Modeling Challenges Facing the Credit Markets?
- Terry Benzschawel (Citigroup)
- Damiano Brigo (DerivativeFitch)
- John Dean (Stark Investments)
- Igor Halperin (JP Morgan)
- Alex Popovici (Citadel)
- Moderator: Dan Rosen (R2 Financial Technologies)
- Corporate Loan and LCDS Pricing and Relative Value
- Terry Benzschawel (Citi)
- Slides
- Available prices on corporate loans are mostly stale and thinly quoted. By analyzing price changes for only liquidly quoted loans, diffusion processes for loans can be deduced and these can be used to estimate expected returns and losses on portfolios of loans. Another aspect of loan valuation is that there is no generally accepted method for computing credit spreads on loans that accounts for their embedded credit dependent prepayment options. I will describe methods for risk-neutral pricing of loans and for computing meaningful measures of loans' credit spreads and durations. Based on those measures, I derive a function for evaluating relative value among corporate loans. I also examined prices of loan credit default swaps (LCDS) relative to their reference loans and the price value of the LCDS cancellability feature. Finally, I will discuss implications of these results for current market prices of loans, LCDS and bond CDS.
- Default Correlation, Cluster Dynamics and Single Names: The GPCL Dynamical Loss Model
- Damiano Brigo (DerivativeFitch)
- Slides
- We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil (2003) to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard "bottom-up" approaches, and to achieve true consistency with single names, improving on most "top-down" loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo, Pallavicini and Torresetti (2006), which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.
- Recovering Credit Portfolio Loss Rates from CDO Tranches
- Rama Cont (Columbia University), with Andreea Minca (Finance Concepts)
- The calibration of (top-down) pricing models for portfolio credit derivatives such as CDOs involves the construction of a risk-neutral jump intensity for the loss process which is compatible with a set of observations of market spreads for CDO tranches. We propose an efficient and stable algorithm to solve this inverse problem by transforming it into a stochastic control probem. Given a set of observations of market spreads for CDO tranches, we construct a risk-neutral default intensity process for the portfolio underlying the CDO which matches these observations, by looking for the risk neutral loss process verifying the calibration constraints 'closest' --in the sense of relative entropy-- to a prior loss process. We formalize the problem in terms of minimization of relative entropy with respect to the prior under calibration constraints and use convex duality techniques to solve the problem. The dual problem is shown to be an intensity control problem, characterized in terms of a nonlinear Hamilton Jacobi system of differential equations which we represent in terms of a nonlinear transform of a linear system and thus easily solved. Our method allows to construct an implied intensity process which leads to CDO tranche spreads consistent with the observations. We illustrate our method ITRAXX index data: our results reveal strong evidence for the dependence of loss transitions rates on the past number of defaults, thus offering quantitative evidence for ``contagion effects" in the risk-neutral loss process.
- Implied Recovery
- Sanjiv Das (Santa Clara University)
- Slides
- The extraction of recovery rates from credit-sensitive securities is an important open problem in the default risk area. Further, the determinants of recovery levels on default are also little understood. We develop a technique for bootstrapping implied risk-neutral forward recovery rate term structures from credit default swap (CDS) spread curves at any single point in time, using only the cross-section of spreads and an additional identification condition. The model accommodates different possible functional relationships between default and recovery to enable simultaneous identification of both hazard rate and recovery term structures under the risk-neutral measure; the underlying fixed-point algorithm is fast and convergent. No time series data is required. We then use indicative CDS spread data from 3,130 firms from January 2000 to July 2002, and extract recovery rates for each firm; these exhibit a strong negative correlation with default probabilities. A principal components analysis of the recovery rates finds one major component (the level of the risk free rate) and another minor one (implied volatility of S&P 500). Market variables are able to explain the variation in the first and second components very well, with R2 s of 90.8% and 35.5% respectively, suggesting that the recovery rate may be modeled on observable factors for trading purposes.
- Replication Based Pricing of Default Contingent Claims
- Bjorn Flesaker (Bloomberg LP), with Peter Carr (Bloomberg)
- Slides
- The standard market model for single name credit default swap pricing is usually represented as a pure reduced form model where default occurs as the first jump of a Poisson process with deterministic risk neutral intensity. We provide conditions under which a static portfolio of standard credit default swaps along with a money market account balance can be used to replicate a broad class of default contingent claims and demonstrate that the resulting no-arbitrage values are consistent with the standard market model, regardless of the dynamics of the default generating process. The replication based pricing operator, as well as the associated survival contingent money market account balance and the replicating CDS portfolio positions, are fully characterized in terms of second order ordinary differential equations (for the continuous maturity limit) and difference equations (for discrete holdings), and examples of their explicit solutions are given.
- Dynamic Hedging of Synthetic CDO Tranches with Spread and Contagion Risk
- Ruediger Frey (University of Leipzig)
- Slides
- We study the risk management of synthetic CDO tranches in a dynamic portfolio credit risk model allowing for spread and contagion risk. The model is constructed and studied via Markov-chain techniques. We discuss the immunization of a CDO-tranche against spread- and default risk and compare the results with hedge ratios as obtained in a Gauss copula model. Moreover, we derive model-based dynamic hedging strategies using the concept of risk minimization and compare to the standard sensitivity-based hedging approaches.
- Pricing, Hedging and Calibrating Credit from the Top Down
- Kay Giesecke (Stanford University)
- Slides
- A credit derivative is a contingent claim on the aggregate financial loss in a portfolio of credit sensitive instruments such as loans, bonds or credit swaps. We analyze the pricing and hedging of credit derivatives using point processes. The recovery at each default is random and events are governed by an intensity that is driven by a set of risk factors. The portfolio loss itself is a risk factor so past defaults and their recoveries influence future loss dynamics. This specification incorporates feedback from events and a dependence structure among default and recovery rates. We show that it leads to analytically tractable transform based pricing, and single name hedging via random thinning. We illustrate the calibration to market index, tranche and single name spreads.
- The Bank as Grim Reaper: Debt Composition and Recoveries on Defaulted Debt
- Michael Gordy (Federal Reserve Board), with Mark Carey (Federal Reserve Board)
- Slides
- We offer a model and evidence that private debtholders play a key role in setting the endogenous asset value threshold below which corporations declare bankruptcy. The model, in the spirit of Black and Cox (1976), implies that the recovery rate at emergence from bankruptcy on all of the firms debt is related to the pre-bankruptcy share of private debt in all of the firms debt. Empirical evidence supports this implication. Indeed, debt composition has a more economically material empirical influence on recovery than all other variables we try taken together. This special role of private debt in the capital structure has important implications for pricing models and risk management.
- Credit Top Down Models: Climbing Down from the Top
- Igor Halperin (JP Morgan)
- Dynamic top-down models for credit portfolios are models of reduced dimensionality useful for pricing and risk management of exotic credit derivatives. In contrast to more traditional bottom-up frameworks, top-down approaches directly specify aggregate (portfolio-level) loss and loss intensity processes as fundamental building blocks of a model. In certain cases, knowledge of single name contributions to the total portfolio credit risk is needed in addition to these aggregate quantities. We discuss practical modeling frameworks for construction of single name dynamics starting with a calibrated portfolio loss process.
- Dynamic Models of Portfolio Credit Risk: A Simplified Approach
- John Hull (University of Toronto), with Alan White (University of Toronto)
- Slides
- We propose a simple dynamic model that is an attractive alternative to the (static) Gaussian copula model. The model assumes that the hazard rate of a company has a deterministic drift with periodic impulses. It is analytically tractable and can be represented as a binomial tree. The jump size plays a similar role to default correlation in the Gaussian copula model. The model can be calibrated so that it exactly matches the term structure of CDS spreads and provides a good fit to CDO quotes of all maturities. Empirical research shows that as the default environment worsens default correlation increases. Consistent with this research we find that in order to fit market data it is necessary to assume that as the default environment worsens jump size increases. We present both a homogeneous and heterogeneous version of the model and provide results on the use of the calibrated model to value forward CDOs, CDO options, and leveraged super senior transactions.
- Pricing and Trading Credit Default Swaps in a Multidefault Setting
- Monique Jeanblanc (Université d'Evry), with Tomasz Bielecki (IIT) and Marek Rutkowski (UNSW)
- Slides
- We address the issue of valuation and hedging of defaultable claims in the market with traded CDSs with different maturities but with the same reference credit name. We derive the dynamics for a family of single-name CDSs in the case of several correlated credit names. Obviously, the fact that the default on a particular name occurs has an impact on the dynamics of CDS written on non-defaulted names. We present some hedging results for defaultable claims
- Time-Changed Markov Processes in Credit-Equity Modeling
- Vadim Linetsky (Northwestern University), with Peter Carr (Bloomberg) and Rafael Mendoza (Northwestern)
- The procedure of time changing a stochastic process allows one to construct new processes from a given process by running it on a new clock that can itself be a non-decreasing stochastic process. Using time changes, we build a new class of analytically tractable credit-equity models that incorporate stochastic volatility, state-dependent jumps, and state-dependent default intensities. Credit products and equity derivatives are valued in a unified fashion in these models.
- The Variation in Implications of Alternative CDO and Credit Portfolio Modeling Techniques
- Donald van Deventer (Kamakura Corporation)
- Slides
- Market convention in modeling CDOs has been to use the copula technology in a Merton framework. This framework, as common as it is, has a number of critical assumptions which have strong implications for valuation of synthetic CDO tranches. We examine those critical assumptions and analyze results for alternative modeling approach, including a reduced form modeling approach when default probabilities are driven by macro economic factors. Results are shown for a hypothetical synthetic CDO where the underlying reference names include 491 BBB rated firms and 9 BB rated firms.