1 Introduction
2 Methods for exposure quantification
3 Derivation of the modified SA-CCR
3.1 Replacement costs
3.2 Potential future exposure
3.2.1 Add-ons for unmargined netting sets
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AO1: The market value of all transactions is zero (\(V_i(t) = 0\)). This assumption implies that the market value of the netting set is zero (\(V_k(t) = 0\)).
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AO2: There is neither received nor posted collateral (\(C_{CE}(t)=0\)).
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AO3: There are no cash-flows within the time period \((t_0,t)\)
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AO4: The evolution of each transaction’s market value follows an arithmetic brownian motion with zero drift.
3.2.2 Add-ons for margined netting sets
3.2.3 Structure of add-on calculations
3.2.4 Aggregation of trade-level add-ons
3.3 Multiplier
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\(\hat{V}_k(t)\) is the (deterministic) market value of the netting set at time t,
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\({C}_{CE}(t)\) represents the cash-equivalent value of net collateral received at t,
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\(\sigma _k(t)\) is the volatility of the netting set at time t and
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Y is defined as a standard normal random variable.
4 Calibration
4.1 Background and general considerations
4.2 Calibration of the modified SA-CCR
5 Empirical analysis
5.1 Methodology
5.2 Results
5.2.1 Results for interest rate swaps
Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|
-2000 | EUR IRS PAY ATM−0.01 5Y | 703.82 | 702.95 |
-2001 | EUR IRS PAY ATM 5Y | 167.68 | 155 |
-2002 | EUR IRS PAY ATM\(+\)0.01 5Y | 11.55 | 11.21 |
-2003 | EUR IRS REC ATM−0.01 5Y | 0.52 | 0.12 |
-2004 | EUR IRS REC ATM 5Y | 55.22 | 43.57 |
-2005 | EUR IRS REC ATM\(+\)0.01 5Y | 490.03 | 491.33 |
-2006 | EUR IRS PAY ATM−0.01 10Y | 2769.08 | 2,789.02 |
-2007 | EUR IRS PAY ATM 10Y | 1125.70 | 1,051.82 |
-2008 | EUR IRS PAY ATM\(+\)0.01 10Y | 324.23 | 311.03 |
-2009 | EUR IRS PAY ATM−0.01 7Y | 1370.16 | 1,363.46 |
-2010 | EUR IRS PAY ATM 7Y | 410.23 | 400.67 |
-2011 | EUR IRS PAY ATM\(+\)0.01 7Y | 57.68 | 69.2 |
-2012 | USD IRS PAY ATM−0.01 5Y | 470.25 | 457.78 |
-2013 | USD IRS PAY ATM 5Y | 120.95 | 96.75 |
-2014 | USD IRS PAY ATM\(+\)0.01 5Y | 20.20 | 13.2 |
5.2.2 Results for FX forwards
Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|
-2015 | EUR/USD FXFWD ATM−20% 1Y | 0.05 | 0.08 |
-2016 | EUR/USD FXFWD ATM 1Y | 81.41 | 80.19 |
-2017 | EUR/USD FXFWD ATM\(+\)20% 1Y | 827.75 | 827.96 |
-2018 | EUR/USD FXFWD ATM−20% 3Y | 12.70 | 17.02 |
-2019 | EUR/USD FXFWD ATM 3Y | 451.54 | 477.00 |
-2020 | EUR/USD FXFWD ATM\(+\)20% 3Y | 2,607.15 | 2675.40 |
-2021 | EUR/JPY FXFWD ATM−20% 3Y | 41.98 | 27.41 |
-2022 | EUR/JPY FXFWD ATM 3Y | 548.06 | 509.16 |
-2023 | EUR/JPY FXFWD ATM\(+\)20% 3Y | 2,431.10 | 2538.73 |
-2024 | EUR/GBP FXFWD ATM−20% 3Y | 22.71 | 45.89 |
-2025 | EUR/GBP FXFWD ATM 3Y | 487.13 | 462.00 |
-2026 | EUR/GBP FXFWD ATM\(+\)20% 3Y | 2489.46 | 2495.68 |
-2027 | EUR/CHF FXFWD ATM−20% 1Y | 0.01 | 0.45 |
-2028 | EUR/CHF FXFWD ATM 1Y | 67.95 | 64.50 |
-2029 | EUR/CHF FXFWD ATM\(+\)20% 1Y | 800.52 | 799.50 |
-2030 | USD/GBP FXFWD ATM−20% 3Y | 41.07 | 83.08 |
-2031 | USD/GBP FXFWD ATM 3Y | 559.32 | 595.09 |
-2032 | USD/GBP FXFWD ATM\(+\)20% 3Y | 2486.28 | 2369.26 |
5.2.3 Results for multi-transaction netting sets
Id | Trade Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|---|
-2033 | -2001 | EUR IRS PAY ATM 5Y | 0.00 | 0.00 |
-2004 | EUR IRS REC ATM 5Y | |||
-2034 | -2001 | EUR IRS PAY ATM 5Y | 1509.91 | 1616.82 |
-2007 | EUR IRS PAY ATM 10Y | |||
-2010 | EUR IRS PAY ATM 7Y | |||
-2035 | -2013 | USD IRS PAY ATM 5Y | 236.43 | 113.26 |
-2001 | EUR IRS PAY ATM 5Y | |||
-2036 | -2012 | USD IRS PAY ATM−0.01 5Y | 362.86 | 290.24 |
-2013 | USD IRS PAY ATM 5Y | |||
-2014 | USD IRS PAY ATM\(+\)0.01 5Y | |||
-2037 | -2019 | EUR/USD FXFWD ATM 3Y | 895.19 | 730.41 |
-2022 | EUR/JPY FXFWD ATM 3Y | |||
-2038 | -2019 | EUR/USD FXFWD ATM 3Y | 462.59 | 415.14 |
-2031 | USD/GBP FXFWD ATM 3Y | |||
-2039 | -2028 | EUR/CHF FXFWD ATM 1Y | 609.61 | 591.44 |
-2031 | USD/GBP FXFWD ATM 3Y | |||
-2040 | -2019 | EUR/USD FXFWD ATM 3Y | 532.95 | 535.98 |
-2016 | EUR/USD FXFWD ATM 1Y | |||
-2041 | -2019 | EUR/USD FXFWD ATM 3Y | 501.31 | 491.82 |
-2004 | EUR IRS REC ATM 5Y |
5.2.4 Results for collateralized portfolios
Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|
-2000 | EUR IRS PAY ATM−0.01 5Y | 16.33 | 10.47 |
-2001 | EUR IRS PAY ATM 5Y | 16.33 | 10.64 |
-2002 | EUR IRS PAY ATM\(+\)0.01 5Y | 16.33 | 10.83 |
-2015 | EUR/USD FXFWD ATM−20% 1Y | 24.17 | 24.02 |
-2016 | EUR/USD FXFWD ATM 1Y | 24.17 | 23.98 |
-2017 | EUR/USD FXFWD ATM\(+\)20% 1Y | 24.17 | 23.94 |
Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|
-2000 | EUR IRS PAY ATM−0.01 5Y | 99.2 | 108.52 |
-2001 | EUR IRS PAY ATM 5Y | 79.71 | 63.98 |
-2002 | EUR IRS PAY ATM\(+\)0.01 5Y | 0.76 | 0.58 |
-2015 | EUR/USD FXFWD ATM−20% 1Y | 15.43 | 15.97 |
-2016 | EUR/USD FXFWD ATM 1Y | 24.51 | 30.85 |
-2017 | EUR/USD FXFWD ATM\(+\)20% 1Y | 35.55 | 43.96 |
5.2.5 Results for non-linear products
Id | Description | CVA (SA-CCR) | CVA (BMM) |
---|---|---|---|
-2126 | EUR/USD FX call option ATM (1Y) | 127.92 | 124.34 |
-2128 | EUR/USD FX put option ATM (1Y) | 127.26 | 115.86 |
-2130 | EUR/USD FX call option ITM (1Y) | 801.10 | 807.98 |
-2131 | EUR/USD FX put option OTM (1Y) | 8.97 | 0.12 |
-2132 | EUR/USD FX call option OTM (1Y) | 0.12 | 0.91 |
-2133 | EUR/USD FX put option ITM (1Y) | 801.10 | 803.44 |