risk methodology in the standardized derivatives market
TRANSCRIPT
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RISK METHODOLOGY
IN STANDARDIZED DERIVATIVES MARKET
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1 Contents
1 Contents ................................................................................................................................... 2
2 General provisions.................................................................................................................... 3
3 Collateral adequacy .................................................................................................................. 3
3.1 Collateral Assessment ....................................................................................................... 3
3.2 Calculation of the Collateral Requirement ....................................................................... 4
3.3 Initial Margin ..................................................................................................................... 4
3.3.1 Market Risk ................................................................................................................ 5
3.3.2 Liquidity risk ............................................................................................................... 9
3.3.3 Credit risk ................................................................................................................... 9
3.4 Settlement value. ............................................................................................................ 11
3.4.1 NPV (OIS) ................................................................................................................. 12
3.4.2 NPV (IRS) .................................................................................................................. 12
3.4.3 NPV (XCCY) ............................................................................................................... 13
3.4.4 NPV (FX Swaps) ........................................................................................................ 14
3.5 Variation margin ............................................................................................................. 14
3.6 Size of Default Fund contribution ................................................................................... 15
4 Interest-rate model ................................................................................................................ 15
4.1 Market data .................................................................................................................... 15
4.2 Model .............................................................................................................................. 16
4.2.1 Model calibration .................................................................................................... 16
4.2.2 Spread calculation ................................................................................................... 17
5 Calculation of risk parameters ............................................................................................... 18
5.1 Statistical risk parameters .............................................................................................. 18
5.2 Dynamic risk parameters ................................................................................................ 19
5.2.1 Interest-rate volatility .............................................................................................. 19
5.2.2 Currency risk rates ................................................................................................... 19
5.3 Limit of fluctuations of the value of the Contract .......................................................... 19
5.4 Parameters of the Contracts concluded with Defaulting Member ................................ 20
5.4.1 FX swap trade parameters ....................................................................................... 20
5.4.2 Conversion rate ....................................................................................................... 20
6 Appendices ............................................................................................................................. 21
6.1 List of currencies accepted as collateral ......................................................................... 21
6.2 Calculation of present value of the Contract .................................................................. 21
6.3 About the credit component of Initial Margin ............................................................... 21
6.4 Scheme of the Initial Margin calculation ........................................................................ 24
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6.5 Scheme of the Settlement value determination ............................................................ 25
6.6 Bloomberg codes for interest-rate derivatives quotes and interest-rate fixings ........... 26
6.7 Decomposition of the Initial Margin ............................................................................... 27
2 General provisions
Risk methodology in the Standardized Derivatives Market (hereinafter the Methodology) has been developed in accordance with the Standardized Derivatives Clearing Rules of CJSC JSCB National Clearing Centre (hereinafter the Clearing Rules) and describes the procedure for determination of risk parameters used by the Clearing Centre to control and manage risks.
The Methodology is disclosed on the website of the Clearing Centre.
The Methodology uses the following terms and definitions:
Volatility – measure of variability of financial indicators. In terms of quantity, it is measured as a standard deviation of changes or relative changes of financial indicators in a certain time interval.
Clearing Centre - Joint-Stock Commercial Bank “National Clearing Centre” (closed joint-stock company).
Clearing Rules - Standardized Derivatives Clearing Rules of CJSC JSCB National Clearing Centre.
Portfolio – totality of effective contracts concluded by certain Clearing Member.
Pool – RUB or USD pool, a contract parameter determining the currency of payment of variation margin in Russian roubles or US dollars respectively.
Settlement value – value of the Contract or of the Portfolio of Contracts, determined pursuant to the clause 3.4 hereof.
Trading day – a day when OTC derivatives are traded.
Any terms not specifically defined herein shall have the meanings ascribed to them by the Clearing Rules, Specifications, and regulative instruments of the Federal Authority.
3 Collateral adequacy
Collateral is deemed to be adequate when the collateralization level of the Clearing Member’s Portfolio is non-negative.
where and Collateral Requirement are determined in the clauses 3.1 and 3.2 of the Methodology respectively.
3.1 Collateral Assessment
Collateral Assessment is determined as follows:
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where:
, – Collateral Cash of the Clearing Member in Russian roubles and Collateral Cash of the Clearing Member in US dollars, recorded on the relevant monetary collateral registers, – RF Rouble / US Dollar exchange rate
determined in accordance with the article 4.1 of the Methodology.
3.2 Calculation of the Collateral Requirement
The size of the Collateral Requirement is determined as follows:
where:
- Initial Margin is a part of the Collateral Requirement, corresponding to the possible costs of the Clearing Centre incurred as a result of the default management procedure and termination of access to clearing services.
- - - of the Collateral Requirement, corresponding to the revaluation of the Settlement value of the Portfolio of the Clearing Member:
( ) ( )
- – sum of Settlement values of Contracts from the RUB pool. - – sum of Settlement values of Contracts from the USD pool. - – accumulated variation margin in Russian roubles under the
RUB Pool Contracts, constituting an accumulated amount of paid/received Variation Margin under the said Contracts.
- – accumulated variation margin in US dollars under the USD Pool Contracts, constituting an accumulated amount of paid/received Variation Margin (negative with minus sign, positive with plus sign) under the said Contracts. If there are any Active Orders (order set { }) of the Clearing Member, the Collateral Requirement is determined as follows:
( ) { }
[( ∑
)]
where – Portfolio of the Clearing Member.
3.3 Initial Margin
The initial margin for the Portfolio (Initial Margin, ) is calculated to cover the variation margin which may arise in the future, and to cover possible costs of the Clearing Centre incurred as part of the default management procedure.
The following risks and approaches to their assessment are notable:
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1. Market Risk a. Risk of changing interest rates (Interest-Rate Risk)
i. Shift-twist-butterfly model ii. Error adjustment of the shift-twist-butterfly model
iii. Error adjustment of the interest rate model b. Risk of changing exchange rates (Currency Risk)
2. Liquidity Risk 3. Credit Risk
Thus, Initial Margin can be defined as a sum of components, each of which covers certain type of the abovementioned risks:
[ ] [ ] [ ]
The appendix 6.4 contains the scheme for calculation of the Initial Margin.
3.3.1 Market Risk
3.3.1.1 Risk factors
Risk factors are the values whose changes are determined in the model described in the article 4 of the Methodology, changes in the Settlement value of the instrument.
The model described in the article 4 of the Methodology uses the following risk factors:
1. Exchange rates (FX) a. US dollar exchange rate: USDRUB Spot
2. Interest rate curves ( ): a. Overnight rates: RUB OIS b. Basis spreads to Mosprime rates: Rate Basis Spread (3m Mosprime vs. RUB
OIS + spd) c. Basis spreads to XCCYrates: XCCY Basis Spread (RUB OIS + spd vs. 3m $
Libor) d. LIBOR rates: 3m $ Libor
Thus, the risk-factor space consists of the US dollar exchange rate and interest rate
curves ( ) and index runs over “liquidity
spots” of each curve.
3.3.1.2 Market risk.
The change of the Portfolio value may be presented as follows:
where j-nd component of the vector from the first summand
[ ] ( [
] ) (
)
– sensitivity of the Portfolio value in case of change of the FX rate by one basis point.
Market component [ ] of the Initial Margin is as follows:
[ ] [ ][ ] [ ][ ]
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where summands in the right section represent interest rate risk and currency risk respectively.
3.3.1.3 Interest rate risk
The component [ ][ ] is calculated on the basis of the shift-twist-butterfly model of interest rate movement and risk factor curve model described in the article 4 hereof. Generally this component can be presented as follows:
[ ][ ] [ ][ ][ ] [ ][ ][ ]
where [ ][ ][ ] is a component calculated on the basis of the assumptions of the above models, and [ ][ ][ ] is an adjustment taking into account the errors of the model (this summand is taken into account in case if model errors play a significant role in calculation of Initial Margin).
Model component
The component [ ][ ][ ] of Initial Margin, determining the size of risk of change of interest rate risk-factor curves is calculated on the basis of the VaR methodology for instruments portfolio. The following assumptions are made:
Evolutions of interest rate risk-factor curves used in the model are independent from each other. This independence assumption is valid due to a transition from the set of risk factors corresponding to rouble curves (OIS, IRS, XCCY) to the set of risk factors constituting a basic curve and spreads thereto (OIS, Rate Basis, XCCY Basis) (see the article 4).
Changes in interest-rate curves are characterized by three major components: , , and .
Given the above assumptions:
[ ][ ][ ]
√∑⟨ [ ] ⟩ ⟨ [ ] ⟩ ⟨ [ ] ⟩
where , , set the possible changes of interest-rate curves (along major components) with pre-set confidence probability:
,
,
where are normalized vectors setting the profile for change of risk-factor curves: ‖ ‖ ‖ ‖ ‖ ‖ , (‖ ‖ ),
– volatility of the relevant components of interest-rate changes, -
volatility multiplier of the -nd curve (determined from the confidence probability level
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and risk assessment horizon ). Risk parameters (vector values) are determined in the clause 5.
In order to separate certain additive components of [ ][ ], the following values are calculated:
[ ][ ][ ] ⟨ [ ] ⟩ [ ][ ][ ]
[ ][ ][ ] ⟨ [ ] ⟩ [ ][ ][ ]
[ ][ ][ ] ⟨ [ ] ⟩
[ ][ ][ ]
Thus:
[ ][ ][ ] ∑ ∑ [ ][ ][ ]
{ }
Error adjustment of the Shift-Twist-Butterfly model
The assessment of [ ][ ] shall use the assumptions of independence of interest-rate curves and of change of interest-rate curves only through three components of shift-twist-butterfly model. Therefore, e.g., there are nonempty Portfolios, for which
[ ][ ]
namely the following Portfolios:
⟨ [ ] ⟩ ⟨ [ ] ⟩ ⟨ [ ] ⟩
Error adjustments related to such facts are defined as follows:
[ ][ ] ∑ [ ]
Risk parameters are determined on the basis of the share of unexplained
dispersion in separation of major components and possible correlation between interest rate curves.
Component of the Initial Margin [ ][ ][ ] is determined as follows:
[ ][ ][ ] ( [ ][ ]
∑ [ ][ ][ ]
{ }
)
where is an indicator of the condition [ ][ ] ∑ [ ][ ][ ] { } .
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Error adjustment of the Interest rate model
The model of interest-rate risk-factor curves, described in the article 4 hereof, is based on the market data in liquidity spots ( ). Values of interest-rate curves in intermediate spots are interpolated using these data. Therefore their assessments and, hence, the prices and risks of the relevant instruments may differ from their “calculated” estimation.
In terms of the Portfolios, this fact leads, for example, to existence of nonempty Portfolios, for which [ ]
, and, therefore, zero components of the market risk described above.
Let us determine the value which takes into account a possible convexity of curves on intervals between liquidity spots:
[ ][ ] ∑ ∑ ∑| ( ) [ ]
|
( )
where ∑ ( ) means summation across all trades from the portfolio with contract
expiration date , risk parameter represents volatility assessment of the
component of change of interest-rate curves at local intervals between liquidity spots.
Component of the Initial Margin [ ][ ][ ] is determined as follows:
[ ][ ][ ] ( [ ][ ]
∑ [ ][ ][ ]
{ }
)
where is an indicator of the condition [ ][ ] ∑ [ ][ ][ ] { } .
Aggregate Interest Rate Risk component
Summarizing, we get the following final components of Interest rate risk:
[ ][ ] ∑ [ ][ ] ,
[ ][ ] ∑ [ ][ ][ ]
{ }
3.3.1.4 Currency risk
The Portfolio sensitivity to FX rate fluctuations ( [ ]) is determined as follows:
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[ ] ( ) ( )
Value of [ ][ ] including the Collateral Сash is determined as follows:
[ ][ ] [ ]
3.3.2 Liquidity risk
This component of the Initial Margin has been designed to cover possible costs associated with market liquidity risk.
The market component of the Initial Margin is determined on the assumptions about perfect liquidity of financial instruments: the default procedures may be implemented within one trading day after the relevant decision.
We introduce the component [ ] which takes into account the potential increase in the time period for performance of the default procedure due to limited liquidity of the Contracts:
[ ] [ ][ ] ∑ [ ][ ][ ]
(√ √ ) √ ,
(√ √ ) √ ,
( [ ]
)
( ⟨ [ ] ⟩
)
( [ ]
)
( | ( ) [ ]
|
)
where and are the horizons for assessment of currency risk and interest rate risk respectively, and risk parameters and determine maximum absolute values of sensitivity ratios , which may be hedged within one trading day without significant influence on the prices of the Contracts.
3.3.3 Credit risk
The component [ ] is designed to take into account credit quality of the Clearing Members when determining the Initial Margin. This component is calculated on the basis of
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the assumption of even distribution of expected losses of the Clearing Centre during the default procedures performed in respect of the Clearing Members (see more details in the clause 6.3):
[ ] ( [ ] [ ]),
In case of non-zero value of the risk parameter , which is individual for each Clearing Member, its value is reported separately to each Clearing Member.
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3.4 Settlement value.
Settlement value of the Portfolio is determined as the sum of Settlement values of the Contracts comprising the Portfolio.
Calculation of the Settlement value of the Portfolio is based on the approach involving determination of Settlement value of the Contracts as net value of discounted cash flows in Russian roubles or foreign currency along discount curves provided in the clause 4 of the Methodology. Variable Amounts under the Contracts are determined on the basis of the relevant forward interest-rate curves, which are determined in the clause 4 of the Methodology. For the Contracts which stipulate settlements in several currencies at once, Settlement value in the currency of the relevant pool is determined as the sum of net discounted cash flows for each currency, converted at the relevant forward rate.
( )
∑ ( ) ( )
∑ ( ) ( ) ( )
( )
∑ ( ) ( ) ( )
∑ ( ) ( )
where
( ) is a discount factor for payments in Russian roubles,
( ) is a discount factor for payments in US dollars,
( ) is the amount of payment in Russian roubles,
( ) is the amount of payment in US dollars
Positive value corresponds to the obligations of the Clearing Centre, while negative value means member’s obligations.
Forward rates ( ) and ( ) are determined as follows:
( ) ( )
( )
( )
( ) ( )
( )
where is RF Rouble / US Dollar exchange rate determined in accordance with the clause 4.1 of the Methodology.
[Note: since the rouble discount factor (under the Model 4) is cross currency–adjusted (moreover, at time intervals less than one year the discount curve is calibrated in line with FX Swaps), the forward curve determined above shall concur with FX Swaps quotes for the time
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intervals less than one year and be in line with XCCY quotes for the time intervals over one year]
3.4.1 NPV (OIS)
Settlement value of the interest-rate swap contract with OIS code is determined as follows:
( ) ( ∑ ( ) ( )
∑ ( )
) ( )
( ) ( ∑ ( ) ( ) ( )
∑ ( ) ( )
) ( )
where are relevant Ratios for calculation of days in the Interestrate Period,
( ) is the expected in the said Interest rate Period accumulated rate, calculated along the forward overnight curve (determined in the clause 4.2 hereof),
is the Fixed Rate under the Contract.
The calculation of the Settlement value of the Contract includes outstanding coupon payments and outstanding premium.
The values are connected with an exchange rate ( ).
3.4.2 NPV (IRS)
Settlement value of the interest-rate swap contract with IRS code is determined as follows:
( ) ( ∑ ( ) ( )
∑ ( )
)
( )
( ) ( ∑ ( ) ( ) ( )
∑ ( ) ( )
) ( )
where are relevant Ratios for calculation of days in the Interest rate Period,
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( ) is the forward curve rate (determined in accordance with the clause 4.2 of the Methodology) for the said Interest-Rate Period,
is the Fixed Rate under the Contract.
The calculation of the Settlement value of the Contract includes outstanding coupon payments and outstanding premium.
The values are connected with an exchange rate ( ).
3.4.3 NPV (XCCY)
Settlement value of the cross currency swap contract with IRS code is determined as follows
( )
∑ ( ) ( ) ( )
( ) ( ) ∑ ( )
( ) ( )
( )
∑ ( ) ( ) ( )
∑ ( ) ( )
( ) ( )
( )
If the obligation of one party to the Contract to transfer ownership of currency to the second party in the amount of the Nominal Amount set for the second party, and the obligation of the second party to pay the first party the Nominal Amount set for the first party have not yet been performed, the above formula is supplemented with the following:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
where are relevant Factor for calculation of days in the Interest rate Period,
( ) is the forward curve rate (determined pursuant to the clause 4.2 of the Methodology) for a given Interest rate Period,
is the Fixed Rate under the Contract,
( ) is the forward rate USDRUB, is the contract expiration date, is the effective date of the contract. The amount includes outstanding coupon payments and outstanding
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premium. The values are connected with an exchange rate ( ).
3.4.4 NPV (FX Swaps)
Settlement value of the FX swap contract is determined as follows:
( )
( ( )) ( )
( )
( ) ( ( ) ) ( ) ( )
If the obligation of one party to the Contract to transfer ownership of currency to the second party in the amount of the Nominal Amount set for the second party, and the obligation of the second party to pay the first party the Nominal Amount set for the first party have not yet been performed, the above formula is supplemented with the following:
( ) ( ( )) ( )
( ) ( ( ) ) ( )
where ( ) is the forward rate USDRUB,
is the Contract’s expiration date,
is the Contract’s effective date,
is the forward rate in the swap,
is the Contract’s underlying rate.
The calculation of the Settlement value of the Contract includes outstanding coupon payments and outstanding premium. The values are connected with an exchange rate ( ).
3.5 Variation margin
Variation margin under the Contract is determined in accordance with Contractual specifications. In this respect:
Settlement value under the RUB Pool Contract is: ( )
Settlement value under the USD Pool Contract is: ( ).
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Also, for the Contract whereunder obligations and claims were met (in this case, any obligations not performed by the Member are not included in the structure of the trade) is set to zero.
Thus, ( ) ( ) ( ),
where .
In addition, if the day is the trade execution date, the value ( ) is set to zero.
3.6 Size of Default Fund contribution
In accordance with the Clearing Rules, a contribution to the Default Fund is calculated as the sum of the minimum contribution to the Default Fund and variable component calculated as follows:
(
),
where
F is the minimum size of the Default Fund, equal to the quantity of the Clearing Members, multiplied by the minimum contribution to the Default Fund,
N is the quantity of the Clearing Members with highest risk volume,
Loss is the size of potential losses of the Clearing Member, calculated at the end of each Trading Day:
where risk parameter Stress is the amount of relative excess of the Member’s loss over Initial Margin.
4 Interest-rate model
4.1 Market data
The model’s input parameters consist of the following sets of market data:
1. Exchange rates: a. USDRUB Spot
2. Interest rates: a. Ruonia:
i. Ruonia ii. RUB OIS: 1w, …, 1y
b. Mosprime: i. Mosprime1M, Mosprime3M, Mosprime6M,
ii. FRA Mosprime3M: 3Mx6M, 6Mx9M iii. IRS Mosprime3M: 1y, …, 5y
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c. FX curve: i. FX Swaps: ON,1W,..,1Y
ii. USDRUB XCCY: 1y, … 5y d. Libor:
i. Libor1M, Libor3M, Libor6M ii. FRA Libor3M: 3Mx6M, 6Mx9M
iii. IRS Libor3M: 1y, …, 5y
The applicable fixing of the USD/RUB rate is the rouble fixing at the Moscow Exchange, calculated pursuant to the Methodology of Calculation of Rouble Fixing at the Moscow Exchange (http://rts.micex.ru/ru/markets/currency/rub-fixing.aspx).
The Appendix 1 contains the Bloomberg codes used to download the quotes for the abovementioned derivatives and values of interest-rate fixings.
4.2 Model
The model represents a set of parameters and approach to estimate of Settlement value of the instruments. In this case, the parameters are discount and forward curves:
1. US dollar curves a. Discount curve b. Libor interest-rate curve
2. Rouble curves a. Discount curve b. Overnight curve c. Mosprime interest-rate curve
In the context of this model and instruments, the estimate of Settlement value means net present value of cash flows (NPV), calculated using the relevant discount and forward curves.
4.2.1 Model calibration
The general approach to model calibration is to determine such of its parameters, i.e. interest-rate curves, that the Settlement values of the instruments for which the model is calibrated would be in line with the market.
4.2.1.1 US dollar curves
The role of the US dollar discount curve and forward curves is played by the curve calibrated using USD 3m FRA and IRS market data, i.e. such curve that the said swaps would have zero Settlement value.
In such case, forward curves are implied curves based on the discount US dollar curve.
4.2.1.2 Rouble curves
4.2.1.2.1 Discount curve
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In the context of this model, the role of the rouble discount curve is played by the curve built using the quotes under the cross currency swap and FX swap contracts (cross-currency adjusted curve).
Given the specifics of the cross currency swap contracts. whose underlying assets are interest rates, Russian roubles and US dollars, a curve can be built using just US dollar curve, as the structure of Contracts implies payment of the Fixed Amount in Russian roubles by one party and payment of the Variable Amount in US dollars by another party.
The FX swap contracts imply an obligation for payment of only fixed amounts (initial payment amount and final payment amount), except obligations for payment of variation margin.
We have to use precisely the cross-currency adjusted curve, as it is the most liquid curve at the time intervals of ON – 5y.
4.2.1.2.2 OIS curve
The OIS curve is a curve built using the quotes for the instruments RUB OIS.
4.2.1.2.3 Mosprime curve
The 3m Mosprime curve is a curve built using the quotes for the instruments RUB 3m FRA and IRS. Mosprime curves of other time intervals are built as implied curves based on the 3m Mosprime curve.
4.2.2 Spread calculation
This stage means formulation of the already built and aligned rouble section of the interest-rate model in the terms of underlying curves and spreads. The purpose of such decomposition is to highlight common and specific risk factors for the instruments in question.
Spread calculation is based on the search for fair (in the context of the built model) implied quotes for the relevant technical instruments constituting swaps involving exchange of two floating rates. Thus, spread is the value added to one of the floating rates so that the value of the swap in the model equals zero.
The role of the underlying curve is played by the RUB OIS curve. The following spreads are reviewed:
1. OIS + spread vs. Mosprime 3m (Rate Basis Spread) 2. OIS + spread vs. 3m $ Libor (Cross Currency Basis Spread)
Thus, in new terms the model is determined by the following parameters:
1. 3m $ Libor 2. RUB OIS Curve 3. RUB Rate basis spread (Mosprime 3m over OIS) 4. USDRUB XCCY basis spread (XCCY Curve over OIS)
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5 Calculation of risk parameters
5.1 Statistical risk parameters
In the below symbols the i index numbers risk-factor curves , and index numbers the major components of curve movement .
Risk parameter Symbol
Volatility multiplier
Exponential weighting ratio
Minimum limitation level of the interest-rate risk corresponding to shift, twist, butterfly-components
Expert adjustment of component volatility of interest-rate curves
Volatility of errors in the shift-twist-butterfly model
Volatility of errors in the interest-rate model
Quantity of instruments with different time intervals, whose quotes constitute risk factors
FX liquidity ratio [ ]
Liquidity ratio [ ][ ]
Currency risk assessment horizon
Interest-rate risk assessment horizon
Member’s credit quality ratio
Ratio connecting currency risk rate and discount rate
Spread for FX swap contracts, in % p.a.
Ratio of the width of Price Corridor and size of the Initial Margin
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5.2 Dynamic risk parameters
5.2.1 Interest-rate volatility
Risk parameters , , which set possible changes of interest-rate curves (along major components) at the moment are determined as follows.
( ) ( ) ,
( ) ( ) ,
( ) ( )
where are normalized vectors setting the profile for change of risk-factor curves: ‖ ‖ ‖ ‖ ‖ ‖ , (‖ ‖ ),
( ) – volatility of the relevant components of interest-rate changes, -
volatility multiplier of i curve (determined from the confidence probability level and risk horizon ).
Volatilities ( ), ( ), ( ) are determined as follows:
( ) ( ( ) )
Calculated volatility ( ) is determined as follows:
[ ( )] ( ) [ ( )]
[ ( )]
The change of curve movement component ( ) is described as follows:
( ) [⟨ ( ) ( )⟩ ⟨ ⟩]
Volatility multipliers are static parameters and are determined on the expert basis using the confidence probability level in calculation of the Initial Margin.
The parameter is a static risk parameter and is determined on an expert basis.
Minimum interest-rate risk levels ,
are static parameters and are
determined on an expert basis.
5.2.2 Currency risk rates
is a static parameter and is determined on the basis of collateral rates effective in the FX market of OJSC Moscow Exchange, determined pursuant to the Methodology of determination of risk parameters of the FX market of OJSC Moscow Exchange.
5.3 Limit of fluctuations of the value of the Contract
Value of the Contract meets the value fluctuations limit if absolute amount of the Settlement value of such Contract does not exceed the product of certain ratio and Initial Margin for such Contract:
where risk parameter is set on an expert basis.
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5.4 Parameters of the Contracts concluded with Defaulting Member
5.4.1 FX swap trade parameters
The underlying rate of a swap trade is determined as follows:
Values of swap points for a swap trade is described as follows (direction is indicated for the Defaulting Member):
[ ][ ]
[ ][ ]
where is a ratio of calculation of the number of days in the time period (pursuant to the ACT/ACT convention),
is a risk parameter determining spread between best buy and sell quotes for a swap trade,
[ ][ ] is a market quote for an overnight swap trade.
5.4.2 Conversion rate
The conversion rate in case of purchase of foreign currency by the Defaulting Member is determined as follows (direction is indicated for the Defaulting Member):
( )
The conversion rate in case of sale of foreign currency by the Defaulting Member is determined as follows (direction is indicated for the Defaulting Member):
( )
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6 Appendices
6.1 List of currencies accepted as collateral
1. List of currencies accepted as collateral: a. Russian roubles (RUB) b. US dollars (USD)
2. The maximum share of foreign currency recorded on the sections of the monetary collateral register of one of the Clearing Members as Collateral Means is set to be 100 (one hundred) percent.
6.2 Calculation of present value of the Contract
The present value of an instrument is the value of the Contract concluded on the terms of the same Specification and with the same set of parameters, except the premium under the Contract and Spreads which are set to zero and with the same NPV.
In its turn, in the context of the set of instruments in question (determined by the Specifications), the value of the Contract means such Fixed Rate that NPV of the Contract equals the said value.
6.3 About the credit component of Initial Margin
This Appendix contains explanations on determination of credit component of the Initial Margin [ ] This component is characterized with the risk parameter , individualized for each Clearing Member. This indicator is calculated by the Clearing Centre as follows:
(
)
where the parameters , , , are interpreted as follows::
– probability that during the default procedure the Clearing Centre’s losses will exceed the value [ ] [ ] (i.e. 1 – = confidence probability of determination of the market component of the Initial Margin).
– downward estimate of expected value of relative excess of the Member’s loss over the Initial Margin [ ] [ ].
– expert risk parameter limiting the value of expected loss of the Clearing Centre for the Portfolio of each Clearing Member relative to the size of its Initial Margin.
– indicator of the Clearing Member’s credit quality, interpreted as probability of the Clearing Member’s default (default of the Clearing Member on its obligations to the Clearing Centre).
Below is the explanation of the above expressions for .
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Let be the random variable equal to the Clearing Centre’s losses on the Portfolio of the - nd Clearing Member. This value may be expressed as follows:
( )
where is the loss of the - nd Clearing Member ( – loss, - profit), –Initial Margin of the Clearing Member’s Portfolio ( )
{
- indicators of the members’ defaults
( ) ( ).
Given:
( )
where is a part of the Initial Margin determined without consideration for credit quality of the Clearing Member ( [ ] [ ]), - “premium” for the Clearing Member’s credit quality ( ).
Having normalized the random value , we get:
( ( ))
We have to note that is affected only by the behavior of at its extremums: , because otherwise . Pursuant to the extreme value theory, distribution of the “tail” of can be approximated using the generalized Pareto distribution. Given the foregoing, and having conducted necessary calculations, we may show that mathematical expectation of has the following downward estimate:
( )
( ) ( )
where
( ) is the probability of excess of the Member’s losses over the Initial Margin,
( ) – probability of default of the Member provided that: .
are parameters of the generalized Pareto distribution approximating the “tail” of the distribution :
-degree of diminution of the “tail” of the distribution
-scale parameter, such that, with approximation accuracy, the expected value of relative excess of the Clearing Member’s losses over the Initial Margin equals:
( ) (
),
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If , then:
( )
Thereafter, for simplification purposes, let us set (rapid diminution of the “tail” of the distribution ). Then we finally get:
( ) ( )
Thus, the “premium” leads to a decrease of the Clearing Centre’s expected loss
(
) times.
On the other hand, the Clearing Centre earns profit in form of a commission fee on the positions of -nd Clearing Member pro rata to the volume of the concluded Contracts and, correspondingly, in crude approximation, pro rata to : . The breakeven performance of the Clearing Centre is equivalent to the following condition:
( )
Therefore it is natural to limit the value of expected loss as follows:
( )
where is an expert ratio, which, on the basis of breakeven performance of the Clearing Centre, must be lower than the share of commission fee from the size of the Initial Margin.
Based upon the above, we derive the necessary precondition for feasibility of the last condition:
The indicator , just as the distribution of the “tail” , generally speaking, depends on the structure of the member’s Portfolio, but due to certain linearity of instruments relative to risk factors it is limited from above by a certain constant depending on the relevant indicators for the distribution of “tails” of risk factors. Therefore the indicator may be the same for all Portfolios of the Clearing Members.
It has to be noted that the risk of concentration of the members’ positions associated with large absolute value ( ), is taken into account when determining the variable portion of contribution to the Default Fund.
24
6.4 Scheme of the Initial Margin calculation
IM
Market risk
(Market)
Liquidity adjustment
(Liquidity)
Credit adjustment
(Credit)
IR(OIS, RateBasis,
XCCYBasis, LIBOR)
FX
ModelModel error adjustments
ShiftTwist ButterflySTB model error
adjustment (ErrorSTB)
IR model erroradjustment
(ErrorIR)
25
6.5 Scheme of the Settlement value determination
Market Data
Risk Factors
Forward rates
Discount curves
Settlementvalue
FX: RUB/USDRuonia: Fixing, OIS
MosPrime: Fixing, FRA, IRSXCCY: FX swap, XCCY swap
LIBOR: Fixing, FRA, IRS
FX: RUB/USDRUB OIS
Rate basis spreadXCCY basis spread
LIBOR IRS
Discount RUB (XCCY-implied)Discount USD (LIBOR-implied)
FX
Ruonia,Mosprime,
LIBOR
USDRUB
RUB OISMosPrime IRS
FX swap, XCCY swapLIBOR IRS
26
6.6 Bloomberg codes for interest-rate derivatives quotes and interest-rate fixings
Ruonia Mosprime USDRUB Curve Libor
Maturity Fixing RUB OIS Fixing FRA IRS FX Swaps XCCY Swaps Fixing FRA $ IRS
0 RUONIA Index MOSKP1 Index
MOSKP3 Index
MOSKP6 Index
US0001M Index
US0003M Index
US0006M Index
1w RRSO1Z Curncy RUB1W Curncy
2w RRSO2Z Curncy RUB2W Curncy
1m RRSOA Curncy RUB1M Curncy
2m RRSOB Curncy RUB2M Curncy
3m RRSOC Curncy RRFR0CF Curncy
RUB3M Curncy
USFR0CF Comdty
6m RRSOF Curncy RRFR0FI Curncy RUB6M Curncy USFR0FI Comdty
9m RRSOI Curncy RRFR0I1 Curncy
RUB9M Curncy
USFR0I1 Comdty
1y RRSO1 Curncy
RRSWM1 Curncy RUB12M Curncy RRUSSW1 Curncy USSA1 Curncy
2y RRSWM2 Curncy RRUSSW2 Curncy USSA2 Curncy
3y RRSWM3 Curncy RRUSSW3 Curncy USSA3 Curncy
4y RRSWM4 Curncy RRUSSW4 Curncy USSA4 Curncy
5y RRSWM5 Curncy RRUSSW5 Curncy USSA5 Curncy
FedFund : FEDL01 Index
27
6.7 Decomposition of the Initial Margin
Components Market risk factors
FX OIS Rate basis XCCY basis Libor Total
Market Risk
Shift
Twist -
Butterfly -
STB model error adjustment
-
IR model error adjustment
-
Liquidity adjustment
Credit adjustment
Total