This is the third of three articles regarding a heuristic approach to measuring counterparty credit risk. In the first part, authorRobert Garzottoexplained the approach broadly. In the second part, he tested the approach using a static portfolio, that is, a portfolio with no new positions added over time. In this part, he tests the approach using a portfolio in which new transactions are added over the course of its life.
COMBINING PRIOR SIMULATION DATA WITH NEW TRANSACTIONS
The principal conclusion that could be drawn from the results of the small portfolio analysis is that with a fixed portfolio and typical1 changes in risk factor levels, the portfolio exposure profile will not change much. But what would be the effect of combining the old simulation results with new transactions? How re-useable are the old simulation results if we experience an extreme shift in risk factor levels?
To answer these and other questions we attempted to simulate what would occur in the "real world" by using a large base portfolio with multiple counterparties combined with new transactions received at the end of the four-day horizon.
The base (i.e., weekend) portfolio that we used in this phase of the analysis was the 3,000 transaction portfolio from which we created the small instrument-specific portfolios. This portfolio contained 1,000 random transactions of each instrument type, evenly distributed across 10 counterparties. The instrument parameters randomized in order to construct the test portfolios may be found in Table 1. Full cross-product netting was assumed within a counterparty and no netting was allowed across counterparties.
The methodology was identical to the heuristic approach described above with one important exception: guided by the small portfolio results, the net present value vectors were not re-centered. To simulate the receipt of new transactions over the course of the week, 300 new transactions were randomly generated across all of the counterparties. The average unexpected exposure (AUE) of the exposure approximation was then compared to the AUE of the benchmark full simulation A. The results of second full simulation B were also compared to the benchmark simulation results as a point of reference. In all cases, a 2000 scenario, 10-step Monte Carlo was performed.
Due to the computational intensity of the calculations, only three of the 10 four-day scenarios were used. However, since each of the 10 counterparties was constructed in an identical fashion, the results are comparable across counterparties. The statistics on the error in AUE relative to the benchmark simulation are shown in Table 2. Note that results were obtained for the total portfolio as well as for the individual counterparties. The results are certainly encouraging. Across all counterparties and all three scenarios (i.e., 30 observations), the average error in AUE relative to the benchmark simulation is only 7.8%. At the total portfolio level, the relative error is virtually negligible (average = 2.52%, standard deviation = 0.33%). The total portfolio result is significant since the internal transfer price for a new transaction would be based on its marginal contribution to total credit risk capital. The goodness of fit between the approximate and full simulation exposure profiles at the total portfolio level is clearly evident in Figure 1.
The results are quite satisfactory for typical changes in risk factor values over the following week. But how re-useable would the weekend NPV vectors be if, over the course of the week, an extremely large shift in risk factor levels occurred? To investigate this, we repeated the experiment using two stress scenarios. Stress scenario one shifted each zero rate in both the U.S. dollar and Deutschmark term structures upward 3.72 standard deviations (99.99% confidence level, one-tailed). In stress scenario two, we again shifted the DEM zero curve upward 3.72 standard deviations but shifted the USD term structure downward by the same magnitude. The corresponding statistics on the error in AUE relative to the benchmark simulation are show in Table 3. As expected, the results are much worse for the stress scenarios than for the typical four-day risk factor perturbations. Clearly, if such a regime shift in risk factor levels were to occur, the entire credit portfolio would have to be re-simulated.
CONCLUSION AND IMPLEMENTATION ISSUES
The results presented above suggest that by leveraging prior simulation results, the time required to calculate global counterparty credit exposure can be substantially reduced without a great loss of accuracy--at least for typical day-to-day changes in risk factor levels. In our case, the heuristic approximation required only one hour versus 11 hours for a full simulation2. The actual savings that can be achieved clearly depend on the turnover rate of the portfolio: a large portfolio with proportionately low weekly transaction flow would benefit the most. Although the results of our investigation are encouraging, a number of the key assumptions need to be stress tested. These assumptions include:
Portfolio composition: our analysis was based on a limited
set of instruments whose NPV was determined by a small
number of risk factors. Would more instruments and risk
factors improve or worsen the results?
Simulation frequency: our analysis assumed that the entire
portfolio would be recalculated on a weekly basis.
However, some firms with particularly large portfolios
containing complex instruments might opt to recalculate
less frequently--perhaps even monthly. This would allow
them to widen the global exposure calculation window to
several days or even a week. How stable is the exposure
profile over horizons longer than a week? What margin of
error is acceptable?
Risk factor dynamics for interest rates: our analysis used a
simple mean-reverting diffusion process for each node in
the interest-rate term structure. How would the results be
affected by the use of systematic risk factors such as
principal components or single factor term structure
models (e.g., Hull/White)?
Since each firm's counterparty credit portfolio is unique, each firm must identify the specific combination of model parameters that yields the optimal trade-off in performance and accuracy.
The 10 four-day scenarios were randomly generated and
could, in fact, include extreme shifts in some of the risk
The one hour reflects the time to simulate the exposure
profiles for the 300 new transactions and combine their
resulting NPV vectors with the stored NPV vectors from
the original 3000 transaction portfolio. The 11 hours
reflects the time to fully simulate the entire 3,300