Deterministic simulation models as insolvency forecasting methods

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Deterministic simulation models as insolvency forecasting methods are important in both banking and insurance regulatory contexts when determining the probability of default of companies , but also when rating the major rating agencies . The assignment of ratings on the basis of deterministic simulations (stress scenarios) is even explicitly mentioned as a permissible procedure for creditworthiness assessment in the Basel II framework , which is otherwise methodologically very open.

One-period models vs. Multi-period models

In the case of multi-period simulations, a development path of the company over a certain period of time is determined ("simulated") on the basis of one or more scenarios. In the (more typical) case of single-period simulations, a time-differentiated modeling of the scenarios is dispensed with; instead, only the immediate effects of certain “extraordinary but plausible shock events” on the company are considered. The individual scenarios can consist of detailed descriptions of the characteristics of individual risk factors as well as - in the case of multi-period simulations - general rules for updating.

Scenario analysis vs. Sensitivity analysis

Depending on whether or not the analyzes are based on specific, identifiable events with precisely specified effects on the modeled risk factors, a distinction is made between scenario and sensitivity analyzes . Furthermore, sensitivity analyzes are typically based on a significantly shorter forecast horizon than scenario analyzes. The characteristics of the risk factors assumed in the respective scenarios can be based on purely fictitious specifications, based on (unfavorable) historical observations (" historical simulation ") or derived from previous model assumptions ("macro models").

Use of deterministic simulation models at banks

However , the deterministic simulation models (stress test models) currently used in the banking context are predominantly not used to create insolvency forecasts or the corresponding determination of " economic capital ", but rather to set investment limits and allocate capital, especially in connection with the modeling of extraordinary risks that arise in Cannot be adequately mapped under conventional VaR approaches. The models used by banks differ significantly between different financial institutions and the results are kept secret. The analyzes mainly relate to liquid markets, more rarely also to non-tradable credit risks and different types of risk (including particularly frequently interest rate risks ).

When using historical scenarios , the following events are particularly frequently used by banks as a basis: “ Black Monday ” (October 1987), global bond market crisis ( 1994) , Asian crisis (1997), Russian crisis - e.g. Partly in combination with the LTCM crisis (1998), terrorist attacks in the USA (2001). It is astonishing how different banks model identical historical events . The scenarios entitled “Black Monday (1987)” consist, for example, of price losses in the S&P 500 share index of 4% to 36%, with a median of 23%. Furthermore, the simultaneous effects assumed for the other markets differ. Only half of the “Black Monday (1987)” scenarios also looked at the bond markets - with interest rates falling in 60% of the scenarios and rising in 40% of the scenarios assumed. Compared to historical simulation, the model-based approach to the definition of the risk parameters has the advantage that it does not depend on a few, possibly random or atypical historical events for modeling future adverse events. On the other hand, the model-based approach requires an explicit modeling of the common distribution function of all risk parameters - for which the theoretical and empirical basis may be missing.

The results of the simulation are the default states determined for the individual scenarios ( solvency vs. insolvency or compliance vs. non-compliance with regulatory requirements) or times (in the case of multi-period considerations). Insolvency forecasts can also be created using conventional empirical-statistical methods on the basis of key figures that are based on the model output (for example the simulated EBIT margin , the equity ratio at the end of the simulation period, etc.).

Criticism of deterministic simulation models

Theoretical weaknesses of the deterministic simulations are the restriction to a small number of scenarios (often only a single scenario is considered) and / or risk factors despite the non-additivity of the usual risk measures , the arbitrary choice of scenarios, their relevance (probability with which a scenario with at least just as great a damage effect occurs) are indeterminate and can differ individually. Further problems with the practical use of the stress test models result from the lack of availability of historical data and, especially in the case of single-period simulations, from the short-term, event-related forecast horizon of the models, in which follow-up and long-term effects are neglected. "However, the accumulation of 'stress events' in particular can jeopardize stability, while isolated shocks can appear relatively unproblematic in themselves."

Some of the aforementioned points of criticism of deterministic simulations could be remedied relatively easily by stochastic modeling of the individual risks. The waiver of this is justified with the individual modeling effort required, especially in the regulatory context, which is considered to be inappropriately high. Furthermore, scenario-based simulation approaches are seen as easier to communicate than stochastic simulation methods, or reference is made to the higher computational requirements.

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  1. ↑ For regulatory deterministic simulation models in the context of insurance companies, see Cummins, Grace, Phillips (1999), BaFin (2004), Lopez (2005, pp. 2f.) And in the context of banks see Deutsche Bundesbank (2003, 2004). For the use of deterministic simulation models by banks, see FRB (1998), Paura, Jokivuolle (2004), Sorge (2004), Basler Committee (2005b) and Lopez (2005).
  2. ↑ see in detail Treacy, Carey (2000) and Carey, Hrycay (2001). The assignment of ratings on the basis of stress scenarios is used in particular when the aim is to achieve stability of the rating judgments across the credit cycle (“ rating through the cycle ”), see Löffler (2004) and Basler Committee (2005a, p. 12 and p. 21ff.) . For the rating of insurance companies using deterministic simulations, see FitchRatings (2003)
  3. ^ See FRB (1998, p. 42) "Stress testing is used routinely by the credit rating agencies, who often assign credit ratings on the basis of a security's ability to withstand various stress scenarios: to qualify for a AAA rating, the security would have to avoid defaulting under a AAA scenario, to quality for a AA rating, the security would have to withstand a AA scenario, and so forth. "
  4. ↑ see Basler Committee (2004, §415): “A borrower rating must represent the bank's assessment of the borrower's ability and willingness to contractually perform despite adverse economic conditions or the occurrence of unexpected events. For example, a bank may base rating assignments on specific, appropriate stress scenarios. "
  5. ↑ This article is based on Bemmann (2007, Section 2.3.3.5).
  6. ↑ see Sorge (2004, p. 1)
  7. ↑ For example, in the scenarios “R 10” / “A 35” / “RA 25” of the Federal Financial Supervisory Authority, a flat rate loss of 10% / 0% / 5% in the value of all fixed-income securities held by the insurance companies and a simultaneous decline in the price of those held Shares subject to 0% / 35% / 20%, see BaFin (2004, o. P.). The stress tests by JPMorgan Chase (2005, p. 73), on the other hand, consist of scenarios in which the individual price developments are specified for around 10,000 individual items.
  8. ↑ The stress test for life insurance companies by FitchRatings (2003, p. 7) is based on a scenario in which real estate prices lose value by 15%, stocks by 35% and fixed-income securities by 12%.
  9. ↑ Basel Committee (2005a, p. 3f.)
  10. ↑ see Deutsche Bundesbank (2003, p. 57ff.)
  11. ↑ see Basel Committee (2005b, p. 4ff.) For the results of a survey on the stress test procedures used by 64 financial institutions from 16 countries
  12. ↑ see Fender, Gibson, Mosser (2001, p. 2ff.), Basler Committee (2005b, p. 4) and Deutsche Bundesbank (2004, p. 80) and Lopez (2005, p. 1)
  13. ↑ see Basel Committee (2005b, p. 1f.)
  14. ↑ see Basel Committee (2005b, p. 30) or by analogy with Lopez (2005, p. 2)
  15. ↑ see Fender, Gibson, Mosser (2001, p. 4)
  16. ^ See FRB (1998, p. 42): “In principle, stress testing could at least partially compensate for the data limitations, estimation problems, and shortcomings in available back-testing methods for credit risk models. Most of the uncertainty within credit risk models (and the infeasibility of backtesting) relates to estimation of the joint probability distribution of risk factors. Stress tests circumvent these difficulties by specifying, albeit arbitrarily, particular economic scenarios against which the bank's capital adequacy might be judged - without regard to the probability of that event actually occurring. [...]. "
  17. ↑ Obviously, the probability of a bank or insurance company becoming insolvent due to adverse effects is much lower than the probability of violating certain regulatory requirements - after all, it is precisely the aim of these regulatory requirements to avoid insolvencies with a high probability, see Paura, Jokivuolle (2004, p. 1809).
  18. ↑ See the cash flow simulation model developed by Cummins, Grace, Phillips (1999) for the prudential bankruptcy forecast of US insurance companies.
  19. ↑ see Sorge (2004, p. 27)
  20. ↑ see Lopez (2005, p. 2)
  21. ^ See Sorge (2004, p. 16): "Most macro stress-tests performed to date have shown that the first-year effects of macroeconomic shocks are very small compared to current levels of capitalization in banking systems across countries. Historical experience, however, suggests that systemic episodes are the result of financial system strains that persist for a number of years and progressively weaken the cushioning capacity of capital. It would be desirable, therefore, to lengthen the horizon of macro stress-tests (so far typically limited to one year) allowing for serially correlated shocks to build up economic imbalances over time […]. "
  22. ↑ Deutsche Bundesbank (2004, p. 81)
  23. ↑ Cummins, Grace, Phillips (1999, p. 424): “The reason for choosing a scenario testing rather than a stochastic approach is that accurate stochastic modeling requires careful estimation of probability distributions, which are likely to vary by company. Such a detailed analysis would not be feasible in a regulatory context where approximately 2000 companies are to be analyzed within a few months' time. "
  24. ↑ Cummins, Grace, Phillips (1999, p. 424): "The scenario approach is also much easier to explain to nontechnical users and thus would be more likely than the stochastic approach to gain widespread acceptance among regulatory personnel."
  25. ↑ see Sorge (2004, p. 6)

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