Editor: Ashish Dev
Published: 07 Dec 2010
Papers in this issue
by Trond Reitan, Kjersti Aas
by Michael Pykhtin, Dan Rosen
by Damiano Brigo, Andrea Pallavicini, Roberto Torresetti
by Frédéric D. Vrins
Promontory Financial, New York
In this issue we present two full-length research papers and two technical reports. The first research paper, "Pricing counterparty risk at the trade level and credit valuation adjustment allocations", is by Michael Pykhtin and Dan Rosen. The paper derives a methodology for allocating to individual trades the counterparty-level credit valuation adjustment (CVA), which is the price of counterparty risk for the entire portfolio of trades with a counterparty. First, the authors show how counterpartylevel CVA can be calculated from the profile of the discounted risk-neutral expected exposure (EE) conditional on the counterparty's default. The authors then draw upon the literature on economic capital (to which they have been regular contributors) to introduce the concept of continuous marginal contribution. Using this method they derive away of calculating marginal CVAcontributions for the case in which there are no exposure-limiting agreements (such as margin agreements) with the counterparty.
These marginal CVA contributions are additive: that is, the sum of each individual trade’sCVAcontributions does add up to the portfolio’sCVA. The authors then further extend the allocation principle for the more general case of collateralized/margined counterparties. In the paper, closed form expressions for EE contributions under the assumption that all trade values are normally distributed are derived. The paper ends with several numerical examples that illustrate the behavior of CVA contributions for both collateralized and non-collateralized cases.
The second research paper, “Credit models and the crisis: default cluster dynamics and the generalized Poisson loss model”, is by Damiano Brigo, Andrea Pallavicini and Roberto Torresetti. The authors carry out a thorough analysis of a model for collateralized debt obligation loss dynamics based on Poisson processes. The model is put to the test with extensive data-based examples from around the crisis period. The paper follows the generalized Poisson loss (GPL) model of Brigo et al from 2007 through the two credit crises, starting with the 2005 auto crisis and culminating in the 2008 subprime crisis. It shows how the GPL approach is able to calibrate all tranches with acceptable accuracy, even in distressed situations. Moreover, the mispricings, if there are any, are shown to be transient, which substantiates the claim that the model is robust and able to withstand different market conditions. One of the main outcomes of applying this model to CDX tranches in stressed markets is the appearance of a bimodal distribution for the expected losses, which the authors interpret as evidence of cluster default dynamics within the underlying pool of names. The authors then proceed to show how to adapt their extended GPL model, which explicitly adds the cluster dynamics to the overall picture in the latter section of the paper. They discuss both the limiting case of homogeneous pools and the specific extensions that address the issues of cluster dynamics and sector dynamics.
A technical report describes a particular practical technique and enumerates situations in which it works well and others in which it does not. Such reports provide extremely useful information to practitioners in terms of saved time and minimizing duplication of effort. The contents of technical reports complement the rigorous conceptual and model developments presented in the research papers and provide a lot of value to practitioners.
The first technical report, “Analytical pricing of basket default swaps in a dynamic Hull–White framework”, is by Frédéric Vrins. The author develops an analytical framework for the dynamic portfolio model proposed by Hull and White in 2008 and shows that, in the specific case in which the jump size of the intensity process in the Hull–White model is constant, many quantities of interest (single-name default probabilities, pairwise default correlations, etc) become available in closed form. For credit portfolios, analytical results are seldom available. Most known results refer to the static setting of the Gaussian copula model in the limiting case of a homogeneous portfolio. The paper adds some analytical insights from a dynamic model perspective. Even though, in practice, the setting of the Hull–White model with constant jump size is likely to be too restrictive for calibration to real market data, the availability of the analytical formulas developed in the paper should be helpful both in developing intuition about the behavior of credit portfolios or related instruments and in providing some inputs (eg, initial guesses) for more intensive numerical calibration procedures in settings excluding analytical tractability (eg, in the case of non-constant jump size).
The second technical report, “A new robust importance-sampling method for measuring value-at-risk and expected shortfall allocations for credit portfolios”, is by Trond Reitan and Kjersti Aas. Efficient Monte Carlo estimation of the downside risk of credit portfolios frequently requires variance reduction techniques (most frequently importance sampling). The authors use Markov Chain Monte Carlo (MCMC) methods to compute the mean shift vector for the systematic factors. They apply their method to two different dependency structures: the widely used normal copula model and the more heavy-tailed t-copula model. The authors compare their method numerically with two competing methods. The comparisons indicate that theMCMCmethod exhibits a similar degree of efficiency to the competing methods in most cases but works better for certain correlation structures.
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