Table of Contents


File

directed_banking_linkages.m

Name

directed_banking_linkages

Synopsis

directed_banking_linkages - Calculates the directed network of banking linkages for n countries between two time instants t1 and t2 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 a directed network, times t1 and t2 must be defined. The thickness of an arrow is then proportional to the amount of net bank flows between regions from t1 to t2. More specifically, an arrow points from A to B if net flows in this direction are positive, calculated as changes in net interbank claims (assets minus liabilities) of banks in A on banks in B, plus net claims of banks in A on non-banks in B, minus net claims of banks in B on non-banks in A.

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

initial_net_bank_claims
Name:
initial_net_bank_claims
Description:

The (i,j) component shows the net bank claims from country i to banks in country j at t1.

Type:
float
Range:
(-inf,+inf)
Dimensions:

NxN matrix (antisymmetric: A == -A')

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

initial_net_non_bank_claims
Name:
initial_net_non_bank_claims
Description:

The (i,j) component shows the net claims from banks in country i to non-banks in country j at t1.

Type:
float
Range:
(-inf,+inf)
Dimensions:

NxN matrix (antisymmetric: A == -A')

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

final_net_bank_claims
Name:
final_net_bank_claims
Description:

The (i,j) component shows the net bank claims from country i to banks in country j at t2.

Type:
float
Range:
(-inf,+inf)
Dimensions:

NxN matrix (antisymmetric: A == -A')

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

final_net_non_bank_claims
Name:
final_net_non_bank_claims
Description:

The (i,j) component shows the net claims from banks in country i to non-banks in country j at t2.

Type:
float
Range:
(-inf,+inf)
Dimensions:

NxN matrix (antisymmetric: A == -A')

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

Outputs

directed
Name:
directed
Description:

A symmetric matrix with null diagonals depicting gross linkages. directed network of banking linkages for N countries between two time instants t1 and t2. Note: values are yes/no flags, represented as 1/0 values, respectively.

Type:
float
Range:
{0, 1}
Dimensions:

NxN matrix, No requirements on symmetry.

  1. Rows represent 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.']);


initial_net_claims =  initial_net_bank_claims+initial_net_non_bank_claims ...
 - initial_net_non_bank_claims';
final_net_claims = final_net_bank_claims + final_net_non_bank_claims ...
- final_net_non_bank_claims';

% Change between t1 and t2
diff_mat = final_net_claims - initial_net_claims;

% If (i,j) element is positive put 1 otherwise 0
directed = diff_mat>0;

num_countries = size(initial_net_bank_claims,1);
% If initial_net_bank_claims and final_net_bank_claims have 0 diagonals
% this is not needed but in any case
for i=1:num_countries
    directed(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.

Very simple net claims graphs:

Bank claims:

 t1:               t2:  
 C1 -20-> C2       C1 <-5- C2
  \      |          \       |
  30    10           15     5
    \   \|/            \   \|/
     `-> C3             `-> C3

Non-bank claims:

 t1:               t2:  
 N1 <-3- N2        N1 <-5- N2
   \     /|\         \     /|\
    13    20         8     40
     \    |           \    |
      `-> N3           `-> N3

 initial_net_bank_claims = ...
 [ 0,  20, 30; 
  -20, 0, 10; 
  -30,-10, 0];

 initial_net_non_bank_claims = ...
 [0, -3,  13; 
  3,  0, -20; 
 -13, 20,  0];

 final_net_bank_claims = ...
 [0, -5, 15; 
  5,  0, 5; 
 -15, -5, 0];

 final_net_non_bank_claims =  ...
 [0, -5,  8; 
  5,  0, -40; 
 -8, 40,  0];

 directed = directed_banking_linkages(initial_net_bank_claims, ... 
 initial_net_non_bank_claims, final_net_bank_claims, ...
 final_net_non_bank_claims);

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.