A Conditional Valuation Approach for Path-Dependent Instruments

Dante Lomibao and Steven Zhu examine the methodology for calculating the potential future exposure of path-dependent derivative instruments

In an effort to improve credit risk management, financial institutions have developed various measures to manage their exposure to counterparty risk. One important measure of counterparty risk is potential future exposure (PFE), which is a percentile (typically 95 or 99 percent) of the distribution of exposures at any particular future date. Credit exposure is the amount a bank can potentially lose in the event that one of its counterparties defaults. The measurement of exposure for derivative products is very important because it is used not only to set up trading limits but also as an essential input to economic and regulatory capital.

The internal economic capital models used by most technologically advanced banks require the calculation of the distribution of the exposure at specified future times. For banks intending to use the internal model method in the new Basel II revised framework on trading activities Basel Committee (2005), specific exposure measures such as the expected exposure (EE) and expected positive exposure (EPE)1 are required in the calculation of the regulatory capital.

This paper focuses on the methodology for calculating the potential future exposure of path-dependent derivative instruments. Unlike loan products, the value of derivatives and other market-driven contracts can change significantly over time as a result of market movements. This may lead to a potential credit exposure with the trading counterparty should it default in the future and its transactions have a positive market value to the bank. Most banks use a variety of methods to manage such risk at the counterparty level, which may include limits on potential exposures, netting, collateral agreements, and early termination agreements. Since most credit limits are based on potential exposure, it is important for a bank to have robust and accurate risk models, as well as systems infrastructure, to quantify the potential exposures of its derivatives positions.

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