Table of Contents


File

undirected_banking_linkages.m

Name

undirected_banking_linkages

Synopsis

undirected_banking_linkages - Calculates the undirected network of banking linkages for n countries based on Fender and McGuire (2010).

Introduction

Fender and McGuire (2010) emphasize the fact that large, international banks tend to have offices in many different countries, hence focusing on banking-group-level balance-sheet risks may ignore important exposures at the individual-office level since these risks are netted out at the group level. Such individual-office frictions may be important, especially during a crisis. A key implication of geographical diversity is that cross-border linkages of individual office locations can determine how shocks are transmitted from one location (country) to another. The authors propose creating undirected and directed networks at the local-office level to assess these risks.

In creating an undirected network, the size of each node is proportional to the stock of cross-border claims and liabilities of reporting banks located in the particular geographical region. The thickness of a line between regions A and B is proportional to the sum of claims of banks in A on all residents of B, liabilities of banks in A to non-banks in B, claims of banks in B on all residents of A, and liabilities of banks in B to non-banks in A. Note that this undirected network is a static depiction of cross-border linkages.

License

=============================================================================

Copyright 2011, Dimitrios Bisias, Andrew W. Lo, and Stavros Valavanis

COPYRIGHT STATUS: This work was funded in whole or in part by the Office of Financial Research under U.S. Government contract TOSOFR-11-C-0001, and is, therefore, subject to the following license: The Government is granted for itself and others acting on its behalf a paid-up, nonexclusive, irrevocable, worldwide license to reproduce, prepare derivative works, distribute copies to the public, perform and display the work.
All other rights are reserved by the copyright owner.

THIS SOFTWARE IS PROVIDED "AS IS". YOU ARE USING THIS SOFTWARE AT YOUR OWN RISK. ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS, CONTRIBUTORS, OR THE UNITED STATES GOVERNMENT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=============================================================================

Inputs

bank_claims
Name:
bank_claims
Description:

The (i,j) component shows the bank claims from country i to banks in country j.

Type:
float
Range:
[0,+inf)
Dimensions:

NxN matrix (not necessarily symmetric)

  1. Rows represent each of N countries.
  2. Columns represent each of N countries.

non_bank_claims
Name:
non_bank_claims
Description:

The (i,j) component shows the claims from banks in country i to non-banks in country j

Type:
float
Range:
[0,+inf)
Dimensions:

NxN matrix (not necessarily symmetric).

  1. Rows represent each of N countries.
  2. Columns represent each of N countries.

non_bank_liabilities
Name:
non_bank_liabilities
Description:

The (i,j) component shows the liabilities of banks in i to non-banks in j.

Type:
float
Range:
[0,+inf)
Dimensions:

NxN matrix (not necessarily symmetric).

  1. Rows represent each of N countries.
  2. Columns represent each of N countries.

Outputs

undirected
Name:
undirected
Description:

A symmetric matrix with null diagonals depicting gross linkages (claims and liabilities) between banks and non-banks in country pairs.

Type:
float
Range:
[0,+inf)
Dimensions:

NxN matrix (symmetric).

  1. Rows represent banks in each of N countries.
  2. Columns represent each of N countries.

Code

% Run warning message
warning('OFRwp0001:UntestedCode', ...
    ['This version of the source code is very preliminary, ' ...
     'and has not been thoroughly tested. Users should not rely on ' ...
     'these calculations.']);


num_countries = size(bank_claims,1);

undirected = bank_claims + non_bank_claims + non_bank_liabilities;
% We need also to add the claims and liabilities from j to i making the
% matrix symmetric
undirected = undirected+undirected';

% Null the diagonal to avoid self-loops
for i=1:num_countries
    undirected(i,i)=0;
end

Examples

NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.

 bank_claims=[100,101,102,103;
              104,105,106,107;
              108,109,110,111;
              112,113,114,115];

 non_bank_claims=[116,117,118,119;
                  120,121,122,123;
                  124,125,126,127;
                  128,129,130,131];

 non_bank_liabilities=[132,133,134,135;
                       136,137,138,139;
                       140,141,142,143;
                       144,145,146,147];

 undirected = undirected_banking_linkages(...
           bank_claims, non_bank_claims, non_bank_liabilities);

References

Fender, I., & McGuire, P. (2010). Bank structure, funding risk and the transmission of shocks across countries: concepts and measurement. BIS quarterly review, 2010, 63-79.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 69-73.