このページは http://www.slideshare.net/AliRaisShaghaghi/ccps-and-network-stability-in-otc-derivatives-markets の内容を掲載しています。

掲載を希望されないスライド著者の方は、こちらよりご連絡下さい。

約1年前 (2015/09/10)にアップロードinビジネス

Among the reforms to OTC derivative markets since the global financial crisis is a commitment to ...

Among the reforms to OTC derivative markets since the global financial crisis is a commitment to collateralize counterparty exposures and to clear standardized contracts via central counterparties (CCPs). The reforms aim to reduce interconnectedness and improve counterparty risk management in these important markets. At the same time, however, the reforms necessarily concentrate risk in one or a few nodes in the financial network and also increase institutions’ demand for high-quality assets to meet collateral requirements. This paper looks more closely at the implications of increased CCP clearing for both the topology and stability of the financial network. Building on Heath, Kelly and Manning (2013) and Markose (2012), the analysis supports the view that the concentration of risk in CCPs could generate instability if not appropriately managed. Nevertheless, maintaining CCP prefunded financial resources in accordance with international standards and dispersing any unfunded losses widely through the system can limit the potential for a CCP to transmit stress even in very extreme market conditions. The analysis uses the Bank for International Settlements Macroeconomic Assessment Group on Derivatives (MAGD) data set on the derivatives positions of the 41 largest bank participants in global OTC derivative markets in 2012.

- CCPs and Network Stability in OTC Derivatives Markets

Seminar 9 September 2015 – Financial Risk and Network Theory

Ali Rais Shaghaghi (Centre for Risk Studies, Cambridge)

With

Prof. Sheri Markose (Dept. of Economics, University of Essex)

Alexandra Heath, Gerard Kelly and Mark Manning (Reserve Bank of Australia)

Views expressed in this presentation are those of the authors and not necessarily those

of the representing organizations - Overview

Motivation

The role of central counterparties

– Collateral

– Netting

OTC data and network reconstruction

Clearing scenarios

Network stability model

Policy messages and future work

2 - Motivation

+$600 Trillion OTC Derivatives

G20’s ambitious program to Improve market infrastructure following the

2007-2008 crisis, central counterparties (CCPs) are being put forth as the

way to make over-the-counter (OTC) derivatives markets safer and sounder,

and to help mitigate systemic risk.

–

Strengthen risk management; reduce interconnectedness

–

However: concentrate risk in one or a few nodes in the financial network and also

increase institutions’ demand for high-quality assets to meet collateral requirements

–

funding and liquidity

Assess implications for stability

Source:

BIS Derivatives Statistics

3 - Structure of Global Financial Derivatives Market

(2009,Q4 202 participants): Green(Interest Rate), Blue (Forex), Maroon ( Equity);

Red (CDS); Yellow (Commodity); Circle in centre Broker Dealers in all markets

Federal Deposit Insurance Corporation (FDIC) Data

4 - The Role of Central Counterparties

A CCP assists institutions in the management

of counterparty credit risk by interposing itself

200

between counterparties to become the buyer

A

B

to every seller, and the seller to every buyer.

These arrangements support anonymous

trading, deepen market liquidity, and generally

maximize the netting of exposures across

160

participants.

180

1) clearinghouses are better able to manage

C

risk than dealer banks in the over-the-counter

derivatives market, and (2) clearinghouses are

better able to absorb risk than dealer

A

B

banks. Adam J. Levitin

40

Policymakers acknowledge that confidence in

CCP

20

underlying markets could be severely tested if

a CCP’s activities were disrupted, leaving

market participants unable to establish new

20

positions or manage existing exposures.

C

5 - Collateral

Replacement cost risk managed through

– Variation margin: exchanged daily usually in cash – to

reflect mark-to-market price changes on participants’

outstanding positions.

– Initial margin: to cover, with typically 99% Confidence level,

potential future exposure arising between the last variation

margin payment and the closeout or replacement of a

defaulted counterparty’s trades

A CCPs initial margin is supplemented with a pool of

resources from all participants known as the default

fund

For systemically important CCPs these fund is

calibrated to withstand the default of its largest two

participants (cover 2)

6 - OTC Derivatives Data

The MAGD(Macroeconomic Assessment Group on Derivatives) data on OTC

derivatives consist of reported balance sheet data

on derivative assets and liabilities for 41 banks

that are involved in OTC derivative trading. (2012

Financial reports)

Tier 1 capital and liquid resources (which we

define here as the sum of cash and cash

equivalents and available-for-sale assets)

($US trillion)

Core

Periphery

Total

(16 Banks)

(25 Banks)

Derivative Liabilities

14.34

12.16

2.18

Derivative Assets

14.48

12.35

2.13

Cash and Cash Equivalents

2.44

1.20

1.25

Available for Sale Assets

5.57

2.83

2.74

Tier 1 Capital

2.39

1.34

1.05

7 - Network Reconstruction

The OTC derivative obligations owed by bank i to bank j

in product-class k 𝑋𝑘

𝑖𝑗

Bank i’s total derivative liabilities in product-class k will be

given by the sum of its obligations 𝐵

𝑋𝑘

𝑗=1 𝑖𝑗,

connectivity priors: 16 core banks 100 % probability

peripheral banks to core banks 50%, peripheral

peripheral 25%

Genetic Algorithm that distributes the aggregate gross

market asset and liability values across bilateral

relationships (Shaghaghi and Markose (2012))

The bilateral gross notional positions are estimated by

multiplying the values in each row of the product matrices

by the ratio of gross notional liabilities to gross market

value liabilities. 𝐆𝒌

The matrix of bilateral net notional OTC derivative

positions is then given by 𝐍𝒌 = 𝐆𝒌 − 𝐆𝒌′

8 - Clearing scenarios and netting

𝑊𝑘

𝑘

𝑖𝑗 = 1 − 𝑠𝑘 𝑁𝑖𝑗,

with CCP 𝑐 𝑊𝑘

𝐵

𝑘

𝑖 𝐵+𝑐 =

𝑠𝑘𝑁

𝑗=1

𝑖𝑗.

𝑠𝑘 = 1 in extreme scenario 3 and 4

Scenario

CCP Service

Per cent centrally cleared, by product class

Scenario 1 Product specific 75 per cent interest rate; 50 per cent credit;

20 per cent commodity; 15 per cent equity;

15 per cent currency

Scenario 2 Single

As in Scenario 1

Scenario 3 Product specific 100 per cent of each product class

Scenario 4 Single

100 per cent of each product class

9 - Netting

Netting efficiency depends on the product and

counterparty scope of a given clearing

arrangement, the profile of positions, and the

margining methodology applied:

Initial Margin at 99 Percent Coverage

Total

Bank-to-bank Bank-to-CCP CCP-to-bank

Scenario 1

942.10

892.88

49.22

0.00

Scenario 2

930.25

892.88

37.37

0.00

Scenario 3

121.82

0.00

121.82

0.00

Scenario 4

80.76

0.00

80.76

0.00

10 - Default Fund Size

In the case of the CCP, the relevant metric is not

capital, but rather the pooled financial resources

in the CCP’s default fund

Table below sets out the size of each CCP’s

default fund in each scenario.

($US billion)

Scenario 1

Scenario 3

CCP1 (Interest Rates)

3.86

5.14

CCP2 (Foreign Exchange)

0.45

3.00

CCP3 (Equity)

1.63

10.83

CCP4 (Credit)

0.84

1.63

CCP5 (Commodity)

0.17

0.87

Total

6.95

21.47

Total encumbrance (default fund and initial margin)

949.05

143.29

Scenario 2

Scenario 4

CCP (Combined)

4.14

11.86

Total encumbrance (default fund and initial margin)

934.39

92.62

11 - Network Stability

Understanding the vulnerability of the system to

failure

Quantify the stability of a network system

Adapt (markose 2013)( Markose, Giansante,

Shaghaghi 2012) eigen-pair method

which simultaneously determines the maximum

eigenvalue of the network of liabilities (adjusted

for Tier 1 capital), to indicate the stability of the

overall system, along with eigenvector centrality

measures.

12 - Network Topology

Scenario 1

Scenario 2

Scenario 3

Scenario 4

The colours of the nodes denote whether the financial institution is a net payer (red) or a net receiver (blue) of variation

margin, while the size of the arrows linking the nodes is proportional to the size of the exposure between them

13 - Model

Populating the stability matrix

𝐵 + 𝑐 financial institutions B Number of banks and

c number of CCPs

𝚯 is a (𝐵 + 𝑐) × (𝐵 + 𝑐) matrix

– where the (𝑖, 𝑗)-th element represents the positive

residual obligation 𝑀𝑖𝑗 from participant 𝑖 to participant 𝑗

as a share of participant 𝑗’s resources

Bank j’s resources, K , include bank 𝑗’s Tier 1

j

capital adjusted for bank j’s contributions to any

CCP default funds. In the case of a CCP, 𝐾𝑗

represents the CCP’s default fund.

14 - Stability Matrix

In hybrid case with separate CCPs the matrix 𝚯 is given as follows:

In case where all position are cleared centrally corresponding

𝑀

0

𝑀12

⋯

𝑀1𝐵

𝑀1𝐶𝐶𝑃1 ⋯

1𝐶𝐶𝑃5

𝐾2

𝐾𝐵

𝐾𝐶𝐶𝑃1

𝐾𝐶𝐶𝑃5

𝑀21

𝑀

0

⋯

𝑀2𝐵

𝑀2𝐶𝐶𝑃1 ⋯

2𝐶𝐶𝑃5

𝐾1

𝐾𝐵

𝐾𝐶𝐶𝑃1

𝐾𝐶𝐶𝑃5

⋮

⋮

⋱

⋮

⋮

⋱

⋮

𝑀

𝚯 =

𝑀𝐵1

𝑀𝐵2

⋯

0

𝑀𝐵𝐶𝐶𝑃1 ⋯

𝐵𝐶𝐶𝑃5

𝐾1

𝐾2

𝐾𝐶𝐶𝑃1

𝐾𝐶𝐶𝑃5

𝑀𝐶𝐶𝑃11 𝑀𝐶𝐶𝑃12 ⋯ 𝑀𝐶𝐶𝑃1𝐵

0

⋯

0

𝐾1

𝐾2

𝐾𝐵

⋮

⋮

⋱

⋮

⋮

⋱

⋮

𝑀𝐶𝐶𝑃

𝑀

𝑀

51

𝐶𝐶𝑃52

⋯

𝐶𝐶𝑃5𝐵

0

⋯

0

𝐾1

𝐾2

𝐾𝐵

15 - Systemic Stress

Liquidity stress

–

can arise at each point in time from the encumbrance of banks’ liquid assets to fund

initial margin and default fund contributions.

o Let 𝐿𝑖 denote bank 𝑖’s liquid assets

o 𝐶𝑖 be bank 𝑖’s total initial margin

o 𝐹𝑖 be bank 𝑖’s contributions to the default fund

𝐶

–

proportion of encumbered liquid assets, given by 𝑖+𝐹𝑖 , is a metric for each bank’s

𝐿𝑖

vulnerability to liquidity stress

Solvency: From Epidemiology : Failure of i at q+1 determined by the criteria

that losses exceed a predetermined buffer ratio, r, of Tier 1 capital

–

is defined in terms of a threshold, 1≤ ri ≤ 0

o For a bank, we assume that only 10 per cent of Tier 1 capital (rBank = 0.1) can be absorbed to

deal with potential derivative losses before the bank is deemed to be in stress. Since a CCP can

use all of its default fund to protect against losses, rCCP=1.

Interconnectedness with counterparties can transmit stress to an institution,

𝑀𝑗𝑖 =

𝑗

𝜃

𝐾

𝑗 𝑗𝑖

𝑖

Incorporating the factors above, the dynamics characterizing the transmission

of contagion in a financial network for a bank can be given by

– 𝑢𝑖𝑞+1 = 𝐶𝑖+𝐹𝑖 − 𝜌𝐵𝑎𝑛𝑘 𝑢

𝑢 𝑢

for q>0

𝐿

𝑖𝑞 + 𝑀𝑗𝑖

𝑗

𝑗𝑞

𝑖𝑞 = 1 − 𝐾𝑖𝑞 𝐾𝑖0

𝑖

𝐾𝑖0

16 - In matrix notation, the dynamics of the system can be

characterized in the following way:

– 𝐔𝑞+1 = 𝐃𝐋𝐢𝐪 − 𝑫𝑺𝒐𝒍 + 𝚯′ 𝐔𝑞 = 𝐐𝐔𝑞

– 𝐔𝑞 is a vector where each element is the rate of failure 𝑢𝑖𝑞

– system stability will be evaluated on the basis of the power

iteration:

𝐔𝒒= 𝐐𝒒𝐔𝟏

The following condition can also be seen to be the

tipping point for the system:

– 𝜆𝑚𝑎𝑥 𝐐 = 𝜆𝑚𝑎𝑥 𝐃𝐋𝐢𝐪 − 𝜆𝑚𝑎𝑥 (𝐃𝐒𝐨𝒍) + 𝜆𝑚𝑎𝑥 𝚯′ < 1.

Right Eigenvector Centrality : Systemic Risk Index

Left Eigenvector centrality Leads to vulnerability

Index

17 - Results of stability analysis

Assuming CCPs hold prefunded resources to

Cover 2 and manage realized uncovered losses

The risk of a systemic problem arising from a

liquidity event in our system, as summarized by

the Liquidity Systemic Risk Index

– (LSRI, 𝝀𝒎𝒂𝒙 𝐃𝐋𝐢𝐪 )

and the probability of a solvency problem arising

from second-round stress, as summarized by the

Solvency Systemic Risk Index (SSRI, 𝝀𝒎𝒂𝒙 𝚯′ ).

LSRI + SSRI < 1 + ρ = 1.1.

18 - Systemic Risk Indices

Scenario 1

Scenario 2 Scenario 3

Scenario 4

Liquidity Systemic Risk Index (LSRI)

0.83

0.83

0.27

0.15

Solvency Systemic Risk Index (SSRI)

Realized 2.67 Volatility

0.16

0.12

0.21

0.30

Realized 3.89 Volatility 0.39

0.31

0.45

0.58

Total Systemic Risk (SSRI+LSRI)

Realized 2.67 Volatility

0.99

0.95

0.48

0.45

Realized 3.89 Volatility 1.22

1.14

0.72

0.73

19 - Systemic Importance and Vulnerability

Systemic Importance

Right Eigenvector Centrality

1.0

1.0

2.67σ

3.89σ

0.8

0.8

0.6

0.6

Banks

CCPs

0.4

0.4

0.2

0.2

0.0

0.0

B2

B1

B1

B6

B4

B5

B2

B1

B2

B9

B3

CC

B1

B8

B3

B3

B1

B1

B3

B2

B2

B1

B1

B4

B6

B5

B2

B1

B9

B3

B2

B1

CC

B1

B8

B3

B3

B1

B2

B7

1

0

3

8

1

P1

2

7

3

6

9

8

1

0

3

8

1

3

P1

2

7

6

8

Systemic Vulnerability

Left Eigenvector Centrality

1.0

1.0

2.67σ

3.89σ

0.8

0.8

0.6

0.6

Banks

CCPs

0.4

0.4

0.2

0.2

0.0

0.0

CC

CC

B8

CC

CC

CC

B1

B7

B4

B4

B2

B1

B3

B6

B1

B1

B2

B2

B9

B2

CC

CC

B8

CC

CC

CC

B1

B7

B4

B4

B3

B2

B1

B6

B1

B1

B2

B2

B1

B9

P3

P1

P2

P4

P5

5

0

1

3

4

3

3

4

6

P3

P1

P2

P4

P5

5

0

3

1

3

4

4

3

0

Ranking of institutions can differ in the respective 2.67 and 3.89 price volatility cases; for example, in Figure 5(a), B6 is

ranked fourth for the 2.67 standard deviation case, while B4 is ranked fourth for the 3.89 standard deviation case.

Eigenvectors normalized to equate highest centrality rank to 1.

21 - Conclusions

Large exposures of CCPs and their extensive interconnections make

them among the most vulnerable institutions in the system

However, given their role and the design of their risk frameworks,

CCPs would not be expected to transmit stress widely through the

system in the event of a shock.

Using real data on banks’ OTC derivatives positions, the analysis in

this work confirms the finding in Heath, Kelly and Manning (2013) that

there is a trade-off between liquidity risk and solvency risk.

Given that Scenario 1 most closely describes the topology that is

likely to be observed in the near term, our analysis underscores the

importance of understanding the stability of networks in which central

clearing and non-central clearing co-exist. We have demonstrated

that in such a scenario, the interaction between liquidity and solvency

risks is particularly important.

We leave to future research, the continued refinement of analytical

techniques to deepen the analysis of how CCPs could transmit stress

under alternative loss allocation mechanisms once prefunded

resources have been depleted.

22