Annex 4 analytical methods

SYMBOL is a simulation model to estimate aggregate losses in the banking sector of a country (or group of countries) in case of a financial crisis. SYMBOL is a Monte Carlo micro-simulation model based on balance sheet and regulatory capital data at individual bank level.

The SYMBOL model is built around the Fundamental Internal Risk Based formula from the Basel III regulatory framework. The riskiness of each bank’s pool of assets is obtained by inverting the FIRB formula*. Individual banks' losses are then generated via Monte Carlo simulation using the Basel FIRB loss distribution function and a correlation matrix representing the common risk factors across European banks. Losses generated in the simulation can then be compared with actual bank capital to check which banks default of remain severely under-capitalized. As the simulation is conducted at individual bank level, any other loss-absorbing or recapitalization tool (e.g. MREL, bail-in, funds) operating at individual bank level can also be modelled. Individual losses remaining after interventions are then aggregated for each simulation run. Given a sufficient number of simulations runs, the aggregate distribution of losses can be estimated. SYMBOL can thus be used to assess the amount of losses that remain uncovered after the intervention of any given set of policy tools, and that could potentially hit public finances. This assessment can be run under various policy scenarios depending on the tools implemented.

The probability distributions obtained from the model cannot be interpreted in terms of “real world” probabilities. This is because the regulatory assumption is that if a bank holds the level of capital prescribed by the formula it should have a probability of default lower than 0.1%, while markets regularly assess the real probability to be higher. As SYMBOL makes use of the regulatory model, its estimates suffer from the same kind of distortion.

This limitation can be overcome by focusing on parts of the distribution of aggregate outcomes which reproduce banking crisis events observed in the real world and by looking at how these outcomes vary under different policy scenarios.

SYMBOL estimations are based on the following assumptions: (1) all risks can be approximated as if they were credit risk; (2) banks report their own risks accurately and in line with the underlying regulatory approach; (3) all events happen at the same time, i.e. there is no sequencing in the simulated events.

Simulation can be run at country level, EU (or EA) level or for any sample of banks. The SYMBOL model is going under continuous revision.

Inputs

The model uses as input data coming from Bankscope/OrbisBankFocus database. Data needed for the SYMBOL model are unconsolidated banks' balance sheet data for a sample of roughly 3,000 EU banks for the period 2006 – 2016 (RWA, total assets, total capital, interbank deposits and loans used only in case contagion is modeled).

Data are processed in order to obtain a reliable dataset. Data quality checks are performed and missing data on capital and risk weighted assets are imputed via robust statistics techniques (FSDA toolbox in Matlab) and by ECS statistics on solvency ratios. Data from the EBA Basel III monitoring exercise (Quantitative Impact Study) are used to adjust for the definition of Basel III capital and RWA.

In case of specific analysis additional data are required. As an example, information on covered deposits is needed to assess the performance of safety net tools. These data are obtained combining data from national Deposits Guarantee Schemes with ECB, Eurostat, or EBA sources.  For liquidity analysis also liquidity buffer, loans, total deposits are needed. For a market risk evaluation data on bonds, shares and other financial assets are needed. Recently, the effect of non-performing loans on losses hitting the banking sector has been introduced.

Results are always rescaled from sample to population via country aggregated ECB statistics on total assets.

Steps of the SYMBOL model:

1. Estimation of the Implied Obligor Probability of Default of the portfolio of each individual bank.
   The main ingredient of the model is the average implied obligor probability of default of a bank. It is a single parameter describing its entire loss distribution. It is obtained by numerical inversion of the Basel IRB formula for credit risk, based on total minimum capital requirements declared in the balance sheet. Individual bank data needed to estimate the implied obligor probability of default are banks' risk-weighted assets and total assets, which can be derived from the balance sheet data.
    

2. Simulation of correlated losses for the banks in the system.
   Given the estimated IOPD, SYMBOL simulates correlated losses hitting banks via Monte Carlo, using the same IRB formula and imposing a correlation structure among banks. The correlation exists either as a consequence of the banks’ exposure to common borrowers or, more generally, to a particular common factor (for example, the business cycle). Each simulation ends when 100,000 runs with at least one default are simulated. This implies to let the model run for few millions of iterations in the case of small size countries and hundreds of thousands iterations for medium-large countries. 

3. Determination of bank failure.
   Given the matrix of correlated losses, SYMBOL determines which banks fail. A bank failure happens when simulated obligor portfolio losses (L) exceed the sum of the expected losses and the total actual capital given by the sum of its minimum capital requirements plus the bank’s excess capital, if any.

4. Output of SYMBOL.
   The output of SYMBOL are matrices with 100,000 rows (number of iterations) and nbanks columns (number of banks in the sample). The value of nbanks varies from few units to more than 1,000 (e.g. Germany).  Recapitalization needs to keep the banks viable are set to be equal to 8% of Basel III RWA and summed up to losses in excess of capital.

5. Aggregate distribution of losses for the whole system.
   Aggregate losses are obtained by summing losses in excess of capital plus potential recapitalization needs of all distressed banks in the system (i.e. both failed and undercapitalized banks) in each simulation run.

* This function is based on the Vasicek model, which in broad terms extends the Merton model to a portfolio of borrowers. See Vasicek O. A., 2002, Loan portfolio value, Risk http://www.risk.net/data/Pay_per_view/risk/technical/2002/1202_loan.pdf and Merton R.C., 1974, On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, 29, 449-470

Main inputs of the SYMBOL model are:

• Total assets
• Total regulatory capital
• Risk weighted assets
• Implied obligors’ probability of default (IOPD): representing the riskiness of the bank’s assets portfolio
• Correlation structure among banks.

Main outputs of the SYMBOL model are:

• Losses of a single bank,

• Aggregated losses in excess of capital plus recapitalization needs of all distressed banks in the system for the whole system

• Effect on public finances of the bail in, resolution funds, deposit guarantee schemes

• Liquidity shortfalls

• Contribution to the systemic risk

The SYMBOL model has proven to be flexible enough to assess the impact of various regulatory/policy initiatives in the realm of banking. In fact, once the model is run one can use the losses distributions (output of the standard model) to evaluate different what-if scenarios and different policy initiatives.

SYMBOL has been used in this way by the European Commission as a tool for ex-ante quantitative impact assessment of a number of legislative proposals and for the assessment of contingent liabilities linked to public support to the EU banking sector.

One typical case is the analysis on the effects on public finances of the bail-in Directive (Bank Recovery Resolution Directive, BBRD). This Directive (European Parliament and Council, 2014) introduces and defines the order of intervention of different safety-net tools which include (i) improved standards on minimum capital requirements and capital conservation buffer set up in the CRR/CRD IV package (ii) bail-in, (iii) Resolution Funds (RF), (iv) Deposit Guarantee Schemes (DGS).

In the latest years Symbol has been used in collaboration with Economic and Financial Affairs Directorate to analyse the stability of the EU 27 banking sector.

• Economy, finance and the euro 
• Taxation