How do I describe the distribution of counterparty credit exposure over time?

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AcadiFi · Accepted Answer

Counterparty credit exposure at any future time is a random variable equal to max(0, MTM) from the surviving party's perspective. Its distribution evolves with the underlying risk factors (rates, FX, equity, credit) and with the trade's structure. For a 10-year interest rate swap with Ironwood Capital Partners, at inception the MTM is near zero. Over time the MTM drifts based on rate moves, producing a distribution that widens then eventually narrows as the swap approaches maturity and remaining cash flows shrink. We typically summarize this distribution with three metrics. Expected exposure (EE) is the mean of the exposure distribution at each future time. Potential future exposure (PFE) is a high percentile, typically 95% or 97.5%. Expected positive exposure (EPE) is the time-average of EE over a horizon, often one year. For an uncollateralized 10y IRS, EE often peaks around year 3-4 and declines thereafter, while PFE peaks earlier and wider. Collateralization dramatically compresses both. Regulatory capital (EAD under the internal model method) uses alpha times effective EPE, where alpha is 1.4 by default. Understanding the time profile is essential for pricing XVAs (CVA, FVA, MVA, KVA) and setting limits. Our FRM Part II CCR sessions walk through Monte Carlo simulations of these profiles with both OIS and historical calibrations.

How do I describe the distribution of counterparty credit exposure over time?

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