margin period of risk

The margin period of risk (MPoR) is a model parameter representing the time interval between the last successful margin exchange and the final close-out or replacement of a portfolio following a counterparty default. It is the key parameter governing residual credit exposure for collateralised portfolios: even with perfect variation margin, the value of a portfolio can change adversely during the MPoR before the surviving party can hedge or replace the defaulted counterparty’s positions. The MPoR is not intended to precisely match the actual close-out timeline but rather to capture, in a single parameter, the aggregate effect of operational delays (margin call, dispute resolution, margin transfer), the time to re-hedge or replace positions, and the liquidation of non-cash collateral.

In the exposure simulation framework, the collateralised positive exposure at time $t$ is modelled as $\max (V_t-C_{t-\text{MPoR}},0)$, where $V_t$ is the portfolio value at time $t$ and $C_{t-\text{MPoR}}$ is the margin that would have been called at time $t-\text{MPoR}$. This creates a “look-back” structure: the exposure at any point depends on the margin state at a prior time, requiring additional simulation grid points. Two approaches exist — a simple look-back method with single additional points, and a “continuous” approach simulating at MPoR-length intervals to capture path-dependent margin features like minimum transfer amounts. The MPoR converts what would otherwise be a long-horizon credit risk problem into a short-term market risk problem, sharing commonalities with VAR methodologies.

Regulatory rules specify the MPoR as 5 business days for repos and centrally-cleared transactions, 10 business days for bilateral OTC derivatives, at least 20 business days for netting sets with illiquid margin or hard-to-replace derivatives, and an additional $N-1$ days if the contractual remargining period is $N>1$ days. However, several real-world effects may not be captured by a simple MPoR assumption: increased volatility following a large counterparty default (following a square-root-of-time rule, doubling volatility would require quadrupling the MPoR), margin disputes extending the effective close-out period, and the question of whether both parties or only the defaulter ceases making payments during the MPoR. The MPoR is relevant for credit exposure (PFE, CVA) but not directly for funding (FVA), since FVA pertains to non-default scenarios where the normal (much shorter) margin posting frequency applies.

Key Details

• Collateralised exposure: ${\text{Exposure}}_t=\max (V_t-C_{t-\text{MPoR}},0)$
• Regulatory MPoR: 5 days (repos, CCPs), 10 days (bilateral OTC), 20+ days (illiquid positions)
• Residual exposure under collateralisation scales approximately as $\sqrt{\text{MPoR}/T}$ relative to uncollateralised exposure over maturity $T$
• “Collateral spikes” occur when cash flows are paid during the MPoR but margin has not yet been received to offset them
• MPoR is a ubiquitous but subjective parameter — it encapsulates operational delay, dispute risk, and volatility conditionality in a single number
• Not relevant for FVA (which assumes normal margin posting frequency in non-default scenarios)

Textbook References

The xVA Challenge (Gregory, 2020)

• Section 7.2.3 / 7.5.2 (referenced from pp. 439—440): Definition of MPoR; relationship to close-out process
• Section 11.3.3 (pp. 306—308): Impact of margin on exposure; EPE reduction under partial, strong, and overcollateralisation (Figure 11.23)
• Section 11.4.2 (pp. 309—310): MPoR in the context of credit exposure vs funding — shorter delay for funding
• Section 15.5.1 (pp. 439—440): MPoR transforms long-horizon credit risk into short-term market risk; dominates over model choice for collateralised portfolios (Figure 15.17)
• Section 15.5.2 (pp. 441—442): Detailed discussion of MPoR assumptions — risk reduction during default, conditionality (volatility increase), disputes, cash flow payments; regulatory MPoR rules
• Section 15.5.3 (pp. 442—445): Modelling approach — look-back vs continuous grid; classical vs improved MPoR model assumptions (Table 15.4, Figure 15.18—15.19)
• Section 15.6.5 (pp. 457—459): Numerical example showing collateralised EPE and PFE with 10-day MPoR; collateral spikes (Figure 15.34)

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