contagion: Contagion Simulations

In NetworkRiskMeasures: Risk Measures for (Financial) Networks

Description

Given a matrix of exposures, a vector of buffers and weights (optional) the functions simulates contagion for all the shock vectors provided. You may choose from the implemented propagation contagion method or create you own propagation method. Details on how to create your own method will be provided in a future version.

Usage

contagion(exposures, 
          buffer, 
          shock = "all", 
          weights = NULL, 
          method = c("debtrank", "threshold"), 
          ...,
          exposure_type = c("assets", "liabilities", "impact", "vulnerability"),
          keep.history = FALSE, 
          abs.tol = .Machine$double.eps ^ 0.2, 
          max.it = min(1000, nrow(v)*10),
          verbose = TRUE)

Arguments

exposures	an adjacency matrix, (sparse) Matrix or an igraph object with the network of bilateral exposures between vertices. By default, the function expects the exposures in the form of an assets matrix in which A -> B means that A has an asset with B. However, you can change that with the parameter exposure_type. When using a matrix, preferably it should have rows and columns names.
buffer	a numeric vector with the capital buffer for each vertex. Values should be in the same row/column order as the network of bilateral exposures. The buffer is not needed if exposure_type = "vulnerability".
shock	a list with the shock vectors. If "all" (the default) the function will run a simulation for the default of each vertex in the network.
weights	default is NULL. You can use a numeric vector of weights to give some economic significance to the measures, like, for instance, the total assets of the nodes.
method	the contagion propagation method. Currently, you should use either "debtrank" for the DebtRank propagation method or "threshold" for the traditional default cascades. The DebtRank version implemented is the one proposed in Bardoscia et al (2015). If you want to use the old "single-hit" DebtRank of Battiston et al (2012), simply provide the argument single.hit = TRUE.
...	other arguments to be passed to the contagion propagation method.
exposure_type	character vector indicating the type of the bilateral exposures. It can be an "assets" network (where A -> B means that A has an asset with B), a "liabilities" network (where A -> B means that A has a debt with B), a (binary) "impact" matrix (where A -> B indicates the relative impact of A in B's capital buffer), or a (binary) "vulnerability" matrix (where A -> B indicates the relative impact A suffers from B's default). The default is "assets".
keep.history	keep all the history of stress levels? This can use a lot of memory, so the default is FALSE.
abs.tol	the desired accuracy.
max.it	the maximum number of iterations.
verbose	gives verbose output. Default is TRUE.

Value

The function returns an object of class "contagion" with the results of the simulation.

References

Bardoscia M, Battiston S, Caccioli F, Caldarelli G (2015) DebtRank: A Microscopic Foundation for Shock Propagation. PLoS ONE 10(6): e0130406. doi: 10.1371/journal.pone.0130406

Battiston, S., Puliga, M., Kaushik, R., Tasca, P., and Caldarelli, G. (2012). DebtRank: Too central to fail? Financial networks, the FED and systemic risk. Scientific reports, 2:541.

Examples

# Loads simulated banking data
data("sim_data")
head(sim_data)

# seed for reproducibility
set.seed(15)

# minimum density estimation
# verbose = F to prevent printing
md_mat <- matrix_estimation(sim_data$assets, sim_data$liabilities, method = "md", verbose = FALSE)

# rownames and colnames for the matrix
rownames(md_mat) <- colnames(md_mat) <- sim_data$bank

# DebtRank simulation
contdr <- contagion(exposures = md_mat, buffer = sim_data$buffer, weights = sim_data$weights, 
                    shock = "all", method = "debtrank", verbose = FALSE)
summary(contdr)

plot(contdr)

# Traditional default cascades simulation
contthr <-  contagion(exposures = md_mat, buffer = sim_data$buffer, weights = sim_data$weights, 
                      shock = "all", method = "threshold", verbose = FALSE)
summary(contthr)

# simulating shock scenarios 1% to 25% shock in all vertices
s <- seq(0.01, 0.25, by = 0.01)
shocks <- lapply(s, function(x) rep(x, nrow(md_mat)))
names(shocks) <- paste(s*100, "pct shock")

cont <- contagion(exposures = md_mat, buffer = sim_data$buffer, shock = shocks, 
                 weights = sim_data$weights, method = "debtrank", verbose = FALSE)
summary(cont)
plot(cont)

Example output

Loading required package: Matrix
  bank     assets liabilities   buffer   weights
1   b1 0.37490927   9.6317127 5.628295 17.119551
2   b2 0.66805904   0.7126552 2.847072  6.004475
3   b3 0.79064804   0.3089983 3.983451  6.777531
4   b4 0.02420156   0.6562193 5.657779  7.787618
5   b5 0.65294261   0.9153901 4.446595  8.673730
6   b6 0.60766835   0.3007373 2.252369  4.708805
Contagion Simulations Summary

Info:
 Propagation Function: debtrank 
 With parameters: 
data frame with 0 columns and 0 rows

Simulation summary (showing 10 of 125 -- decreasing order of additional stress):
 Scenario Original Stress Additional Stress Original Losses Additional Losses
      b55          0.1102             0.280            58.4             235.8
      b28          0.0638             0.182            63.5              99.3
      b84          0.0236             0.117             7.6              65.7
      b69          0.0133             0.114            13.0              36.6
      b75          0.0099             0.113             9.6              30.5
      b33          0.0243             0.088            27.4              33.6
     b120          0.0099             0.077             8.4              18.1
      b77          0.0067             0.065             9.4               8.9
      b74          0.0161             0.064            14.4              27.9
     b101          0.0070             0.060             9.3              17.1
 Additional Defaults
                  17
                   8
                   2
                   2
                   2
                   2
                   2
                   1
                   3
                   2
Contagion Simulations Summary

Info:
 Propagation Function: threshold 
 With parameters: 
data frame with 0 columns and 0 rows

Simulation summary (showing 10 of 125 -- decreasing order of additional stress):
 Scenario Original Stress Additional Stress Original Losses Additional Losses
      b55          0.1102             0.273            58.4             221.1
      b28          0.0638             0.167            63.5              88.4
      b84          0.0236             0.098             7.6              62.0
      b69          0.0133             0.096            13.0              34.1
      b75          0.0099             0.095             9.6              28.1
     b120          0.0099             0.075             8.4              17.0
      b27          0.0173             0.059            20.5              18.8
      b74          0.0161             0.056            14.4              26.1
     b101          0.0070             0.052             9.3              15.6
      b80          0.0084             0.051             9.2               7.5
 Additional Defaults
                  16
                   7
                   2
                   2
                   2
                   2
                   3
                   3
                   2
                   1
Contagion Simulations Summary

Info:
 Propagation Function: debtrank 
 With parameters: 
data frame with 0 columns and 0 rows

Simulation summary (showing 10 of 25 -- decreasing order of additional stress):
     Scenario Original Stress Additional Stress Original Losses
 23 pct shock            0.23              0.25             182
 22 pct shock            0.22              0.25             174
 21 pct shock            0.21              0.25             166
 24 pct shock            0.24              0.25             190
 20 pct shock            0.20              0.25             158
 25 pct shock            0.25              0.25             198
 19 pct shock            0.19              0.25             150
 18 pct shock            0.18              0.25             142
 17 pct shock            0.17              0.24             134
 16 pct shock            0.16              0.24             127
 Additional Losses Additional Defaults
               179                  14
               173                  13
               167                  12
               185                  15
               161                  11
               191                  16
               155                  10
               149                  10
               142                  10
               136                  10

NetworkRiskMeasures documentation built on March 13, 2020, 3:24 a.m.