300 J. Roy
5 The disaggregated approach
Under the disaggregated approach, the income statement of each credit union is simu-
lated using six stochastic variables: namely, the net interest income, loan losses, other
income, other expenses, operating expenses and operational losses. Overall, these six
variables are meant to capture interest rate risk, market risk, credit risk and opera-
tional risk. Once the income statements are simulated, the balance sheets of the credit
unions are computed. Should the capital beunder the regulatory requirement, then a
demand for subsidy at the guaranty fund will be generated. After the total demand for
subsidies is computed, the financial statements of the guaranty fund are simulated.
Trajectories simulating 15 consecutive years are run using 50 000 trials in order to
obtain the distribution of the level of capital of the fund and thus estimate its solvency
over the 15-year horizon.
Let us now examine in more details how the six stochastic variables were modelled.
Special attention was devoted to credit risk, as it is believed to be the most important
source of risk. Thus, the loan portfolio of each credit union was in turn divided into
ten types of loans, namely: consumer loans, mortgages, investment loans, commercial
loans, agricultural loans, institutional loans, lines of credit to individuals, commercial
lines of credit, agricultural line of credit and institutional lines of credit. In turn,each
of these ten types of loans was divided into three size categories, namely: below
$100 000, between $100 000 and $1 000 000, and above $1 000 000. Now, foreach of
these 30 credit segments, five historical parameters were available: the probability of
default (PD), the exposition at default (EAD), the loss given default (LGD), the number
of loans in the segment (N) and the correlation factor with a global latent economic
factor (ρ). A Merton-type model is then used. First, the value of the latent economic
factor is drawn and then the PD of each segment is conditioned on its value. Secondly,
the number of defaults (ND) in a segment is generated with a binomial distribution
using the number of loans in the segment N and the conditional PD. Finally, the loan
losses are obtained as the product of the number of default ND, the exposure at default
EAD and the loss given default LGD. The five other stochastic variables are simulated
using normal distributions using expected values and standard deviations. Two sets
of assumptions are used: a base case using historical values and a stressed case where
the standard deviations were increased by 50 % to represent higher risks. Finally,
a correlation structure was modelled. Serial correlation factors were assumed for
the latent economic factor (0.5) to represent business/credit cycles, for the operating
expenses (0.5) and for net interest revenue (0.5) to represent the inertia of these. A
negative cross correlation factor (− 0 .55) was also introduced between net interest
revenues and operational losses.
Following the simulation of the financial statements of the credit unions, those
of the guaranty fund are generated. The fund has two types of revenues: revenues
obtained from investing its assets and premiums collected from the credit unions. It
has three main types of expenses: fixed administrative expenses, payment of subsidies
to the needing credit unions and taxes on its profit. Stochastic values were generated
for investment income, which were correlated to the latent economic factor, and for
the subsidies paid through the simulation described in the above subsection. Finally,