Replacement cost and credit exposure are the market-risk components of counterparty credit risk that define what could potentially be lost in the event of a counterparty default. They are the core inputs to the CVA calculation and, more broadly, to all xVA terms since the portfolio’s current and future value drives funding positions, collateral amounts, initial margin, and capital requirements.
Credit exposure is defined as the positive part of the portfolio value: exposure = max(V, 0). This asymmetry reflects the fact that if the counterparty defaults when the portfolio value is positive (an asset), the surviving party has a claim that may not be fully recovered; if the portfolio value is negative (a liability), the surviving party still owes its contractual payments. Replacement cost is closely related: it represents the cost of entering into an equivalent transaction with another counterparty, and it is the amount referenced in default-related contractual features such as close-out netting. In practice, replacement cost may exceed the simple mark-to-market due to bid-offer spreads and illiquidity, especially for non-standard or long-dated instruments.
The future value of a derivative portfolio is uncertain, and characterising the distribution of future exposure is central to counterparty risk quantification. Key metrics include: expected positive exposure (EPE), which is the expected value of the positive part of the portfolio value at each future date and is the primary input to CVA; and potential future exposure (PFE), which is a high-quantile (e.g. 95% or 99%) measure used for credit limit management. The relationship between current valuation and these future exposure metrics is one of the main challenges in xVA computation, requiring simulation of market risk factors over the entire lifetime of the portfolio.
Key Details
- Exposure = max(V, 0) is a one-sided measure: positive value represents a claim on the defaulted counterparty; negative value does not release the surviving party from its obligations.
- Replacement cost may include real costs such as bid-offer spreads and rehedging costs for illiquid portfolios. It may also include xVA terms such as CVA, creating a recursive valuation problem.
- PFE is used for credit limits (binary risk control); EPE is used for CVA (continuous risk pricing). These are complementary approaches.
- Exposure is typically assumed independent of counterparty default (no wrong-way risk), though this is an approximation.
Textbook References
The xVA Challenge (Gregory, 2020)
- Section 3.3.2 (pp. 57—58): The current portfolio value (MTM) is the starting point for all xVA components. It defines credit exposure (directly), funding position, initial margin (via variability of valuation), collateral amount, and capital. Two key questions: what is the current valuation, and what is the valuation in the future?
- Section 3.3.3 (pp. 58—59): Replacement cost defines the entry point into an equivalent transaction with another counterparty. Documentation aims to reference replacement costs as objectively as possible. Exposure = max(V, 0); positive value is a claim on a defaulted counterparty, negative value does not release the surviving party. Replacement cost may include xVA terms, creating recursion.
- Section 3.1.5 (pp. 48—50): PFE characterises the potential future exposure at a given confidence level and is compared against credit limits. For derivatives, PFE requires quantitative modelling incorporating transactions, portfolio composition, market variables, and risk mitigants.
- Section 17.2.2 (pp. 487—490): EPE(t, u) = E[V(t, u)^+] is the expected positive exposure at time u, discounted to t. It is the market risk input to the standard CVA formula (Eq. 17.3).