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Copyright Infopro Digital Media Services Cutting edge: Regulation Revisiting SA-CCR In this article, Mourad Berrahoui, Othmane Islah and Chris Kenyon propose a comparison for SA-CCR, termed Revisited SA-CCR, which reconstructs SA-CCR in a self-consistent and appropriately risk-sensitive way by cashflow decomposition in a three-factor Gaussian market model identified from SA-CCR itself. This framework can guide banks in resolving ambiguities in their SA-CCR interpretation he recent request for comments from the Office of the Comptroller dynamics. Table C shows EEPE versus moneyness and direction as of Decem- of the Currency (OCC 2018) offers an opportunity to address ber 5, 2018. The EEPE was calculated using a one-factor Hull-White model T observations on the Basel standardised approach for measuring identified from SA-CCR (mean reversion 0.05, flat volatility 0.0189). Note counterparty credit risk exposures, SA-CCR (BCBS 2014b, 2018a), and may that although the supervisory factor isServices 50bp, this translates directly into a inform other jurisdictions (BCBS 2018b). Our major observations include Hull-White volatility of 189bp. a lack of self-consistency for linear trades; a lack of appropriate risk sen- Thus, SA-CCR does not have appropriate risk sensitivity because (i) eco- sitivity (zero positions can have material add-ons; moneyness is ignored); nomically zero positions can have material add-ons and (ii) moneyness is and dependence on economically equivalent confirmations. Other signifi- ignored, which can exclude material risk differences. cant observations we address include the ambiguity of risk assignment (ie, the Dependence on economically equivalent confirmations. Trade-level requirement for a single primary risk factor) and a lack of clear extensibility. add-ons in SA-CCR are defined as: Our observations about the SA-CCR’s properties, and the point sugges- trade (a) (a) AddOn = ıi SF d MFi tions of other authors (BCBS 2013), highlight principles by which we could i i i (a) assess SA-CCR, namely: appropriate risk sensitivity (the same exposure for SF captures risk-factorMedia volatility for asset class a, ı is 1 for direction (a˙) the same economics; positive exposure for non-zero risk), transparency, con- and MF is the maturity factor. The adjusted notional d incorporates a sistency and extensibility. The scope of this article is limited to non-option duration measure. interest rate products, for which these issues are most significant. Our objec- We can construct zero add-ons for any IRS with maturity T > 1 year, tive is to provide a comparison of the current SA-CCR with a Revisited SA- where T and 2T are in the same maturity bucket, as follows: a receiver (rate R) amortising swap with notional 3(e0:05T /(e0:05T CCR (RSA-CCR) that is consistent with the existing structure and principles 1))N between today and T , and then notional (e0:05T /(e0:05T 1))N of SA-CCR but free of the observations discussed above. This RSA-CCR can guide banks in resolving ambiguities in their SA-CCR interpretation during between T and 2T (N is an arbitrary positive number); a payer (rate R) swap with maturity 2T and notional 2(e0:05T /(e0:05T implementation. Longer proofs, additional details and derivations can be found in theDigital as- 1))N ; accepted version of this paper and the technical appendix (Berrahoui et al a forward start (starting at T with maturity 2T ) receiver (rate R) swap with notional (e0:05T /(e0:05T 1))N ; 2019), both available on SSRN. a payer swap (rate R) with maturity T and notional (1/(e0:05T 1))N . (IR) Observations on SA-CCR The adjusted notional (ie, time average) d for the first two swaps is the same: 2(e0:05T /(e0:05T 1))N . They are in opposite directions, so their Our observations on SA-CCR are for linear instruments, which we illustrate net add-on is zero. The maturity factor (MF) is the same for the thirdand using interest rate swaps (IRSs). We demonstrate these can be material for fourth trades: 1 (as T > 1). This is also true of the supervisory factor (SF(IR) simple situations, and then we describe RSA-CCR. in the regulation), which is 0:005 for both trades. The sum of direction and Lack of self-consistency for linear trades. Economically equivalent adjusted delta is: positions have different capital requirements.Infopro For example, a vanilla IRSor 0:05T 0:05T 0:05 2T a set of forward rate agreements (FRAs) with the same strike have different X (IR) e e e ıi d = N add-ons (see table A). Thus, SA-CCR is not self-consistent. i e0:05T 1 0:05 i=3;4 Lack of appropriate risk sensitivity. We illustrate two aspects of this 0:05T 1 1 e here: that economically zero positions can have material add-ons, and that N e0:05T 1 0:05 moneyness is ignored. The latter is probably more important; for example, = 0 moneyness produces systematic risk for existing positions when the general level of rates changes. So, the net add-on for the third and fourth trades is also 0. Now the net To illustrate the first case, consider an IRS that is economically hedged economics over all four trades is 0 for T to 2T , but it is a net receiver swap with a set of FRAs. There is a non-zero add-on despite there being zerorisk from 0 to T with flat notional N (e0:05T 1)/(e0:05T 1) = N . (see table B). Thus, SA-CCR is dependent on economically equivalent confirmations, Non-at-the-money (non-ATM) swaps have the same regulatory add-ons and this is not an objective of the standard (unlike leverage ratio capital). but can have wildly different effective expected positive exposures (EEPEs), even whenCopyright using very simple dynamics (see table C). RSA-CCR: cashflow and model-based SA-CCR SA-CCR ignores the moneyness of linear derivatives, although non- To address our observations about SA-CCR we propose a cashflow- and ATM swaps can have wildly different EEPEs even when using very simple model-based comparison for SA-CCR, which we call Revisited SA-CCR risk.net 1 Cutting edge: Regulation A. Equivalent derivatives positions with different add-ons For an ATM swap with start date Ts, end date Te and notional N , we show Instrument SA-CCR add-on in theorem 1 that the volatility of the present value of the swap (assuming a ATM swap 3,934,693 flat discount curve with zero rate) is: FRA replication 3,433,691 Split at 3Y 3,654,794 HW aTs aTe ATM(0) = N (e e ) ATM swap is 10Y USD, 100M notional. Split means a 3Y swap and a separate forward starting swap a (starting at 3Y for 7Y), with the same fixed rate as the ATM 10Y swap Given the relation (1) between theoretical add-on and trade volatility, we B. Material add-on for zero economic position obtain a model-based add-on for the ATM swap, identical to the SA-CCR Instrument SA-CCR add-on add-on: ATM net of FRA replication 1,646,936 aT aT 2HW e s e e Position is an ATM swap 10Y USD, 100M notional hedged by a strip of FRAs AddOntrade = N 3p2 a e aTs e aTe C. EEPE versus moneyness and direction calculated using a one-factor Hull-White = N SFIR model identified from SA-CCR; mean reversion 0.05, flat volatility 0.0189 Servicesa Instrument Pay Receive Thus, SA-CCR and BCBS (2014a) implicitly identify an appropriate model. ATM+500bp 5,778,184 3,898,079 ATM+100bp 4,271,792 3,707,917 Given that SA-CCR and BCBS (2014a) can be interpreted as using a one- ATM 3,903,699 3,668,881 factor Hull-White model, we extend this to a three-factor model to take into ATM 100bp 3,539,968 3,634,569 account the correlation structure of the different maturity zones in a later ATM 500bp 2,166,837 3,577,668 section. Correlations between add-ons are mapped to correlations between Fwd start ATM 1y–10y +500bp 4,712,043 4,891,493 zero-coupon bonds. Fwd start ATM 1y–10y +100bp 3,932,090 3,931,231 Fwd start ATM 1y–10y 3,737,350 3,691,418 Identity of SA-CCR and a one-factor Hull-White for a single matu- Fwd start ATM 1y–10y 100bp 3,542,763 3,451,756 rity bucket. Here,Media we provide details to establish a formal correspon- Fwd start ATM 1y–10y 500bp 2,766,729 2,495,425 dence of ATM swap add-ons between SA-CCR and a one-factor Hull-White Under SA-CCR, the top five trades have the same add-ons, as do the bottom five. ATM swapis10Y model. This correspondence being established, the regulatory parameters cor- USD. All instruments have a USD100M notional responding to model parameters are as shown in the previous section. This process also shows how to extend SA-CCR consistently to non-ATM trades (RSA-CCR). We pick the model by identifying it from the SA-CCR stan- in order to take moneyness into account. dard itself using the link between trade level add-ons and the volatility of A one-factor Hull-White model (Hull & White 1990) has short rate the present value of the trade in BCBS (2014a). Basing RSA-CCR on cash- (r(t)) dynamics, given by (2) above, so the dynamics of a zero-coupon bond flows automatically solves the lack of self-consistency, lack of appropriate risk P (t; T ) price are: sensitivity, dependence on economically equivalent confirmations, and accu-Digital a(T t) rate risk assignment.
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