Methodologies - Witz® Credit Risk Management & Advisory Group, LLC

Probability of default model validation
Probability of default (PD) is the conventional measure of single-name credit risk. The validation of PD thus plays a key role in developing robust internal rating systems. At Witz, we employ alternative methods, including point-in-time and through-the-cycle approaches, to validate estimates for PDs. In backtesting a PD model, we not only employ common statistical methods, such as the binomial test, the normal test and goodness-of-fit type tests, but also utilize the Bayesian technique to induce risk assessment in the absence of sufficient historical default data. The latter approach can leave the opportunity to our clients to determine the posterior distribution of a PD, given zero realized defaults in a rating category.

Default correlation estimation
Default correlation is a crucial parameter in any credit portfolio management. It would be a daunting task, however, to estimate pair-wise default correlations. Conforming to industry standards, we estimate the default correlation (via asset value correlation) with the "common factor" (or "conditional independence") approach to make parameter reduction. This techinque uses semi-analytic method to save the computational intensity of Monte Carlo simulations. Further, we choose the factor sensitivities such that they are in line with observed default behavior. This method requires fewer assumptions and relatively less demanding in terms of default related data. We use maximum likelihood principle to determine default probabilities (conditional on realized factor value) and factor sensitivities.

Risk aggregation and loss distribution
One of the critical step in credit portfolio analysis is determining the loss distribution. With a loss distribution in hand, it is straightforward to measure the amount of credit enhancement necessary for a tranche to attain a given credit rating. In essence, the construction of a loss distribution amounts to the aggregation of individual credit risk, incorporating default dependence/correlation among individual obligors. The information about the loss distribution can be used in risk management (e.g., Value At Risk calculation) and portfolio optimization, regulatory compliance (Economic capital), valuation of correlation product (CDO). At Witz, we provide solid methods in estimating loss distribution function for both homogeneous and heterogeneous portfolios. Most methods used in practice are simulation-based, which could be time consuming and error-accumulating. We focus on analytical approaches, such as saddlepoint and extended version of Vasicek model. These approaches have the advantage of easy and fast computation and can be used to derive the shape of the tail of the loss distribution without resorting to Monte Carlo simulation. Moreover, it can be shown that the saddlepoint approximation method is accurate and robust in cases where standard methods perform poorly.

Economic capital calculation//Basel II
The Basel II Capital Accord has brought a focus on credit risk management by aligning risk management with globally accepted best practices, and making risk management a more risk-sensitive task. Since a bank should spend most of its capital for profitable investments, there is a strong incentive to minimize the capital it holds. Hence, one of the main problems of risk management in a financial institution is to find the balance between holding enough capital to be able to withstand financial distress, on the one hand, and minimizing economic capital to make profit, on the other. At Witz, we help our clients strike this balance by providing economic capital estimates under alternative assumptions and methods. The "lower bound" and "upper bound" numbers can be judged by clients as "aggressive" or "conservative".

Securitization and structured product modeling
The current financial crisis has triggered the dispute about the role of structured finance products and their modified forms. In our view, part of the problems comes from erroneous model assumptions, such as static and constant correlation (as in Gaussian copula model, an industry standard). Many securitized products including CDOs are structured based on the assumption of a certain degree of diversification in the performance of the underlying collateral. The decline of housing prices at the national level, however, could and did increase the correlation to unprecedented levels. The collateral underlying the structured CDOs were all exposed to the same systemic shock all of sudden. The time-varying correlation is a key factors that complicate the valuation of CDOs. Worst of all, different correlation parameters are implied for different tranches in the Gaussian one-factor copula. This means that we assume different loss distribution for the same portfolio depending on which tranche we look at! This is a glarying consistency. Wrong assumptions on default correlation values can be fatal for large scale correlation trades. At Witz, we strive to improve the standard model by implementing several cutting-edge techniques. One such model is the inverse Gaussian copula with stochastic factor loadings. These models produce very convincing and consistent results, albeit at the expense of some of numeric efficiency.

Deriving credit spread from volatility skew (in extended Merton's framework)
The power of Merton's model is its insightful linkage between credit market, equity market and option market. Equity and option market provide a useful and most likely more liquid venue for price discovery of credit risk. Under Merton's framework, an option on equity of a company is a compound option on the asset of the company. As an implementation of structural model, Witz adopts an approach of leading academic and industry experts (e.g. John Hull) and derive the credit spread from implied volatility surface. Compared to the traditional approach in implementing Merton's model, the inputs to the model are much simpler. All required to imply a credit spread are two points on the volatility surface. This approach is particularly appropriate for firms that are known (or rumored) to have significant off-balance sheet liabilities.

Measuring counterparty risk
Counterparty risk, which is the focal point for market participants, policy-makers, regulators, accountants, tax authorities and many others, is the risk that a party to an over-the-counter (OTC) derivatives contract may fail to perform on its contractual obligations, causing losses to the other party. Losses are usually quantified in terms of the replacement cost of the defaulted derivatives and include, beyond mid-market values, the potential market impact of large and/or illiquid positions. We believe that there are two critical measurements for this risk: 1) Current exposure (CE) - the current value of the exposure to a counterparty, which is relatively easy to compute; 2) Potential future exposure (PFE) - the maximum amount of exposure expected to occur on a future date with a high degree of statistical confidence. For example, the 95% PFE is the level of potential exposure that could be exceeded with only 5% probability. The estimation of PFEs requires sophisticated models to simulate exposures in market scenarios on various future dates. At Witz, we assist our clients in their specification of the PFE model and its ongoing validation, which are of paramount importance for monitoring counter party risk.

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