Standard & Poor's Ratings Services' ratings are opinions of creditworthiness based on our analysis. Ratings are not precise probabilities of default but rather a relative ranking of creditworthiness. One important tool we use in assigning ratings, but by no means the only one, is quantitative modeling. This report summarizes our definition of models, briefly describes what Standard & Poor's models are and are not used for, and discusses in general terms our view on methods of combining qualitative and quantitative considerations in the ratings process. The paper concludes with a discussion of our views on some distinctions we see between models suitable for ratings analysis and models more suitable for use in valuation, portfolio optimization, and risk measurement. 
A quantitative model is a controlled view of certain real world dynamics that is used to infer the likely consequences of some prespecified assumptions under various circumstances. However, in the process of moving from inputs to outputs, a model may not capture all the nuances of the real world. The distinctive feature of a quantitative financial model is that it is a quantitative calculation based on one or more assumptions. Models are not black boxes of revealed truth but merely numerical expressions of some view of how the world would be likely to behave. The models used in finance rely on assumptions about the behavior of people, organizations, acts of the natural world, and the use of other models by market participants. Quantitative financial models embody a mixture of behavioral psychology, statistics, numerical methods, and subjective opinions. The physical sciences have laws of nature called "theories," that observation or experiments can verify or disprove. In finance, however, there are merely statistically significant tendencies and patterns, and there are always exceptions that do not fit these patterns. These exceptions do not mean that a given model is not useful. Rather, all quantitative financial models are necessarily generalizations that events in the real world will sometimes contradict. Because mathematicians, scientists, and engineers have developed powerful techniques for solving certain types of equations, quantitative financial analysts tend to express the underlying financial dynamics and assumptions as the same type of mathematical equations, and employ analogies to physical laws. This enables the financial models to use the same techniques from the physical sciences to compute the numerical solutions to these financial equations. Different assumptions and different intended uses will in general lead to different models, and those intended for one use may not be suitable for other, unintended uses. Weaker performance under such circumstances does not necessarily indicate defects in a model but rather that the model is being used outside the realm for which it was optimized. In our view, the test of a financial model is how suitable it is for its intended use, which involves a simultaneous test of assumptions, inputs, implementation, and usage. We believe that quantitative financial models can be very useful tools for analyzing credit risk. 
The intended uses of quantitative financial models include valuation, portfolio selection and optimization, risk measurement, and stress testing. Some features of any one model type might be incompatible with other model types. For instance, some riskmeasurement models, such as the Baselmandated 10day 99% ValueatRisk (VaR) model, assume the probabilities of certain hypothetical future events and infer the likely consequences if these events occur. The VaR model is calibrated based on the assumption that market behavior in the near future will usually be similar to the recent past. Other riskmeasurement models, collectively called stress tests, infer the likely consequences in assumed severe but plausible scenarios, without necessarily assigning any numerical probability to the scenarios. These stresses are calibrated based on the assumption that the market may occasionally behave very differently than it has in the recent past. An important distinction, in our view, between these two models is that, broadly speaking, the former addresses a bad day in a normal market, whereas the latter addresses an abnormal market. Models used for different purposes could call for different assumptions. For example, because our assessment of creditworthiness is not a unique number but rather a band of expected performance, a credit rating model might calculate a modest range of values consistent with a specified stress assumption, whereas a valuation model would in general produce a much tighter range of values consistent with the current market with no extra assumed stresses. Also, the number of assumptions needed can depend on the characteristics of the intended use. As an example, consider a complex interest rate option. A standalone valuation model for the option is based on the assumed dynamics of the yield curve. If that same option is embedded in a highyield corporate structured note, a model for valuing the incremental change in the note's price due to the embedded option must make additional assumptions about the relationship between interest rates and the issuer's credit spread, and about the likelihood of suboptimal option exercise in different hypothetical yield curve scenarios. A model for estimating the incremental change in creditworthiness of that same structured note due to the same embedded option must make additional assumptions about both the likely option exercise behavior of the issuer in different hypothetical credit stress scenarios and the likely relationships between credit scenarios and interestrate scenarios. Financial risk consists of various components such as credit risk, franchise risk, liquidity risk, market risk, operational risk, and political risk. Most of the models Standard & Poor's uses are intended for our analysis of credit risk  the likelihood and probable magnitude of credit events under different economic conditions. These models can concern many aspects of credit risk, including:
It's important to note that rating committees assign ratings based on qualitative and quantitative assessments. Where applicable, model outputs can provide relevant, useful information for purposes of a committee's analysis. Many quantitative tools can be classified as either true models or rulebased calculations. True models (such as Standard & Poor's CDO Evaluator and LEVELS) make assumptions about possible future scenarios, while rulebased calculations (such as cashflow "waterfall" computations) compute the consequences of a given set of inputs without making any assumptions. For example, suppose that, in one particular scenario of a model, a CDO would collect $100. A rulebased cashflow tool could calculate how that hypothetical $100 would be paid out to the various tranches and accounts through the waterfall spelled out in the contract. For a model intended for stress tests, some important features, in our view, may include:
For models intended for risk measurement in lessextreme conditions, such as VaR, some important features, in our view, may include:
Valuation models assume some relationships between some observed "calibrating" prices for liquidly traded instruments and the theoretical price of a lessliquid instrument, and they infer this unobserved price. Here, the analogous important features, in our view, may include:
Predictive models, such as those used for investment and portfolio optimization, attempt to strike a balance between some measure of risk and a prediction of future reward. In general, these do not target market mispricing. Rather, they attempt to evaluate the market price of risk. They can address the entire market or a particular segment, or they can aim at a particular risk profile. Some key features, in our view, may include:
Statistical arbitrage models attempt to find and exploit perceived errors in the market consensus. In some sense, this is the opposite of a valuation model. The goal is, in CAPM (capital assets pricing model) jargon, to enhance alpha, either with a single security or on the portfolio level. In our view, key features may include:

For certain securities, the use of quantitative financial models can be an important tool in the rating process. The models Standard & Poor's uses are built to embody our assumptions and are specifically designed for use in our ratings process. These models can differ from those intended for other purposes and from those embodying different assumptions. We may use these models earlier in the ratings process than qualitative analysis, or later, or simultaneously, depending on our view on how best to analyze a particular aspect of credit risk.
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