This is the first of three articles regarding a heuristic approach to measuring counterparty credit risk. In this part, author Robert Garzottobroadly explains the approach. In the second part, he tests the approach using a static portfolio, that is, a portfolio with no new positions added over time. In the final part, he tests the approach using a portfolio in which new transactions are added over the course of its life.
INTRODUCTION
Driven by the stick of narrowing margins and lured by the carrot of regulatory capital relief, many banks have implemented sophisticated market risk measurement systems based on Monte Carlo simulation--the de facto standard in market risk measurement methodology. Now, many of these same firms have turned their attention the more complex and computationally onerous problem of measuring and managing the counterparty credit risk in their trading portfolios. In recognition of the methodological synergies between measuring market and credit risk, many firms have sought to leverage their existing investment in market risk management technology. Unfortunately, many have found their market risk systems woefully inadequate to tackle the long-term simulations required to measure global counterparty credit exposure.
However, there exists a relatively straightforward heuristic approach to measuring counterparty credit exposure that can be easily built on top of existing market risk systems that are based on Monte Carlo simulation. The general idea is to reuse the results of prior Monte Carlo simulations; consequently, each transaction would have to simulated only once. Such an approach would have enormous benefits, not the least of which would be obviating the need to invest in additional hardware and software. Moreover, the approach could be adapted to provide near real-time credit risk information to transactors. This would enable traders to retrieve pre-deal information such as limit availability or even the required credit spread based on the potential transaction's marginal contribution to global credit exposure.
This article is organized into three sections: the first describes the heuristic simulation approximation in detail; while the remaining two sections, which will be serialized in DW, analyze the quality of the approximation vis-à-vis full simulation by applying the approach to randomly generated transaction/portfolio data. A well-known commercially available risk engine was used to generate the exposure profiles.
APPROACH
The overall approach is described in detail below:
* Step 1: Calculate current and future potential exposure for the global portfolio. Suppose our counterparty credit risk management system (system) calculates (via multi-step Monte Carlo simulation) a term structure of exposure for its entire global trading portfolio over the weekend. For each instrument in the portfolio and each scenario, the system stores the associated vector of changes in net present value (delta-NPV vector)--a vector dimensioned by the number of time steps in the exposure profile. The system also stores the scenarios themselves; or rather, the perturbations in the values of each risk factor in each scenario and time step in the simulation.
* Step 2: Simulate current and future NPV for new transactions. At the close of business on Monday, the bank would like to recalculate its global counterparty credit exposure to reflect any changes in its portfolio. First the system retrieves the end-of-day risk factor values and marks to market (model) any new transactions that entered the portfolio during the day. Next, it simulates the values of the new transactions at each desired time step in the future and stores the resulting NPV vectors. But rather than deriving completely new scenarios, the system applies the risk factor perturbations stored from the weekend run to the new risk factor values. This enforces consistency with the results of the weekend simulation.1
* Step 3: Calculate current and future NPV for old (weekend) transactions. Again, the system retrieves the new risk factor values and marks to market (model) all the old transactions from the weekend portfolio that have not matured over the course of the day. However, to simulate the transactions forward in time, the system simply applies the stored delta-NPV vectors to the new mark to market (model) of each transaction. The intuition here is that the future potential exposure distribution is being "re-centered" to reflect the new risk factor values. This is illustrated in Figure 1. As illustrated in the diagram, if the MTM of the portfolio increases from one day to the next, we might expect the exposure profile to shift upwards as well. Again, the system stores the resulting NPV vectors.
* Step 4: Calculate term structure of exposure. The system retrieves the stored NPV vectors for the new transactions and the weekend portfolio and aggregates them according to the specified global netting hierarchy.
1 One obvious problem with this approach is that the
perturbations may be highly "level-dependent" as a result
of mean reversion, the magnitude of a risk factor
perturbation is a function of the difference between the
current value and the target level. If risk factors have
changed significantly from the close of business on Friday,
the stored perturbations may be inconsistent with the new
risk factor values.
This week's Learning Curve was written by Robert Garzotto is a principal consultant at the Capital Markets Co.in New York.
