globals [deposit-bank default-probability loan failure number-of-informed information-probability time-after-default counter fund deposit-at-failure] turtles-own [liquidity draw? informed] breed [passives passive] breed [actives active] breed [companies company] ;**********************************************************************TO SETUP********************************************************************* to setup ca setup-patches setup-turtles set deposit-bank 5 ;; 5 represent the bank reserve set failure 0 ;; 1 if the company is failed, 0 otherwise set number-of-informed 0 set default-probability 0.001 ;; the initial value of probability deafult is 0,01% reset-ticks set time-after-default 0 ;; this variable is use for the graph of information diffusion set counter 0 ;; this counter is used to fix the financing every 100 ticks do-plots ;; plots the bank activity do-graph ;; plots the information diffusion end to setup-patches ask patches [ if ((pxcor < 4) and (pxcor > -4) and ;; we create a yellow square in the centre of the world that represents the bank (pycor < 4) and (pycor > -4)) [ set pcolor yellow ] ask patch 1 0 ;; we assign to the patch of coordinates x=1 and y=0 the label "BANK" [ set plabel "BANK" ] set plabel-color black ] end to setup-turtles create-passives portion_passives * number_of_investors ;; we create the actives and passives investors create-actives (1 - portion_passives) * number_of_investors ask passives [ set color green set size 1.2 setxy random-xcor random-ycor if pcolor = yellow [ set xcor (xcor - 9)] set shape "person" set liquidity 1 set informed 0 ;; 1 if informed, 0 otherwise ifelse show-liquidity? [set label liquidity] [set label ""] ] ask actives [ set color red set size 1.2 setxy random-xcor random-ycor if pcolor = yellow [ set xcor (xcor - 9) ] set shape "person" set liquidity 1 set informed 0 ;; 1 if informed, 0 otherwise ifelse show-liquidity? [set label liquidity] [set label ""] ] create-companies 1 ask companies [ set color brown set size 4 set shape "factory" setxy 14 14 ] end ;*************************************************************************TO GO************************************************************************ to go tick move-turtles deposit/draw financing default do-plots if failure = 1 [set time-after-default (time-after-default + 1) ;; if comapny default, it plots the graph of the information diffusion do-graph] if deposit-bank = 0 [stop] end to move-turtles if failure = 0 or (failure = 1 and fund = 0) [ ;; if the company is not failed or is failed and the loan is 0: ask passives [ right random 360 fd 3.5 ] ask actives [ right random 360 fd 3.5 ]] if failure = 1 and fund != 0 [ ask actives [if liquidity = 0 [if informed = 0 [ set color blue ;; the not informed investors have color blue set information-probability random-float (1000) ;; we establish that the probability of became informed is a number included in a range from 0 to 999 if information-probability < ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * ;; if the random number is below the effective probability of became informed, the investors bacame informed and they assume color orange (fund / deposit-at-failure) [set informed 1 set color orange set number-of-informed (number-of-informed + 1) set xcor (random-float(6) - 3) set ycor (random-float(6) - 3)] if information-probability > ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [right random 360 fd 3.5 ]]] if liquidity = 1 [if informed = 1 [set xcor xcor set color orange] if informed = 0 [set color blue set information-probability random-float (1000) if information-probability < ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [set informed 1 set color orange set number-of-informed (number-of-informed + 1) set xcor xcor ]] if information-probability > ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [right random 360 fd 3.5 ]]] ask passives [if liquidity = 0 [if informed = 0 [set color blue ;; the not informed investors have color blue set information-probability random-float (1000) ;; we establish that the probability of became informed is a number included in a range from 0 to 999 if information-probability < ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * ;; if the random number is below the effective probability of became informed, the investors bacame informed and they assume color orange (fund / deposit-at-failure) [set informed 1 set color orange set number-of-informed (number-of-informed + 1) set xcor (random-float(6) - 3) set ycor (random-float(6) - 3)] if information-probability > ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [right random 360 fd 3.5 ]]] if liquidity = 1 [if informed = 1 [set xcor xcor set color orange] if informed = 0 [set color blue set information-probability random-float (1000) if information-probability < ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [set informed 1 set color orange set number-of-informed (number-of-informed + 1) set xcor xcor ]] if information-probability > ((0.5 - ((0.5 - 0)*((0 - deposit-bank) / (0 - deposit-at-failure)))) * 1000) * (fund / deposit-at-failure) [right random 360 fd 3.5 ]]]] end to deposit/draw if failure = 0 or (failure = 1 and fund = 0) [ ask passives [ set draw? (random 10) ;;random number included in a range from 0 to 9 if ((xcor < 4) and (xcor > -4) and ;;if the turtle goes on the yellow patch: (ycor < 4) and (ycor > -4)) [set xcor (xcor - 8) ;;moves the turtle outside the bank ifelse liquidity = 1 [set liquidity (liquidity - 1) ;;if the turtle has 1, it deposit 1 increasing the deposit-bank of 1 set deposit-bank (deposit-bank + 1) ] [if draw? < 8 [set liquidity (liquidity) ;;if the turtle has 0, it can draw or do nothing set deposit-bank (deposit-bank) ] ;;for 80% of case the passive turtle do nothing, for the 20% of case it draw if draw? > 7 [set liquidity (liquidity + 1) set deposit-bank (deposit-bank - 1) ]]] ] ask actives [set draw? (random 10) ;;random number included in a range from 0 to 9 if ((xcor < 4) and (xcor > -4) and ;;if the turtle goes on the yellow patch: (ycor < 4) and (ycor > -4)) [set xcor (xcor - 8) ;;moves the turtle outside the bank ifelse liquidity = 1 [set liquidity (liquidity - 1) ;;if the turtle has 1, it deposit 1 increasing the deposit-bank of 1 set deposit-bank (deposit-bank + 1) ] [if draw? < 2 [set liquidity (liquidity) ;;if the turtle has 0, it can draw or do nothing set deposit-bank (deposit-bank) ] ;;for 20% of case the passive turtle do nothing, for the 80% of case it draw if draw? > 1 [set liquidity (liquidity + 1) set deposit-bank (deposit-bank - 1) ]]] ]] if failure = 1 and fund != 0 [ ;;when company failes the informed investors go to the bank for draw the unitary amount ask actives [ if ((xcor < 4) and (xcor > -4) and (ycor < 4) and (ycor > -4)) and (deposit-bank > 1) [if liquidity = 0 [set liquidity (liquidity + 1) set deposit-bank (deposit-bank - 1) set xcor random-float(6) + 5 ;;when they draw, they go out the bank set ycor random-float(6) + 5] if liquidity = 1 [set xcor random-float(6) + 5 ;;if their liquidity is equal to 1 they don't go to the bank set ycor random-float(6) + 5]] if ((xcor < 4) and (xcor > -4) and (ycor < 4) and (ycor > -4)) and (deposit-bank > 0) and (deposit-bank <= 1) [if liquidity = 0 [set liquidity (liquidity + deposit-bank) set deposit-bank (deposit-bank - deposit-bank) set xcor random-float(6) + 5] set ycor random-float(-6) - 5 ] if ((xcor < 4) and (xcor > -4) and (ycor < 4) and (ycor > -4)) and (deposit-bank = 0) [if liquidity = 1 [set xcor random-float(6) + 5 set ycor random-float(6) + 5]]] ask passives [ if ((xcor < 4) and (xcor > -4) and ;;when company failes the informed investors go to the bank for draw the unitary amount (ycor < 4) and (ycor > -4)) and (deposit-bank > 1) [if liquidity = 0 [set liquidity (liquidity + 1) set deposit-bank (deposit-bank - 1) set xcor random-float(-6) - 5 ;;when they draw, they go out the bank set ycor random-float(-6) - 5] if liquidity = 1 [set xcor random-float(-6) - 5 ;;if their liquidity is equal to 1 they don't go to the bank set ycor random-float(-6) - 5]] if ((xcor < 4) and (xcor > -4) and (ycor < 4) and (ycor > -4)) and (deposit-bank > 0) and (deposit-bank < 1) [set liquidity (liquidity + deposit-bank) set deposit-bank (deposit-bank - deposit-bank) set xcor random-float(-6) - 5 set ycor random-float(-6) - 5] if ((xcor < 4) and (xcor > -4) and (ycor < 4) and (ycor > -4)) and (deposit-bank = 0) [if liquidity = 1 [set xcor random-float(-6) - 5 set ycor random-float(-6) - 5]]]] ask passives [ifelse show-liquidity? [set label liquidity] [set label ""]] ask actives [ifelse show-liquidity? [set label liquidity] [set label ""]] end to financing if failure = 0 [if counter < 100 [set counter (counter + 1)] if counter = 100 [ask companies [set loan (loan + (deposit-bank * financing-percentage)) ;; the bank grant a percentage of deposit to the company every 100 ticks set deposit-bank (deposit-bank - (deposit-bank * financing-percentage)) set fund (loan) ] set counter 0]] if failure = 1 [set loan 0] ;; if company fails the loan goes to 0 end to default if ticks > 60 [if deposit-bank < 0.3 * number_of_investors [set deposit-bank (deposit-bank + (loan * 0.3)) ;; if bank deposit goes below o,3 * number_of_investors, the bank require the restitution of 30% of funding granted set loan (loan - (loan * 0.3)) set default-probability (default-probability + 0.001)] ;; and the probability of default rise of 0.001 ] ask companies [if random 1000 < default-probability [set failure 1 set color red set deposit-at-failure (deposit-bank)]] ;; after default, company became red end to do-plots set-current-plot "Bank activity" ;; title of graph set-current-plot-pen "deposit-bank" ;; variable plotted plot deposit-bank set-current-plot-pen "loan" ;; variable plotted plot loan end to do-graph set-current-plot "information diffusion" ;; title of graph plotxy time-after-default number-of-informed ;; variable plotted end @#$#@#$#@ GRAPHICS-WINDOW 205 10 644 470 16 16 13.0 1 10 1 1 1 0 1 1 1 -16 16 -16 16 0 0 1 ticks CC-WINDOW 5 484 976 579 Command Center 0 BUTTON 17 34 81 67 NIL Setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 100 34 163 67 NIL Go T 1 T OBSERVER NIL NIL NIL NIL SLIDER 19 83 191 116 number_of_investors number_of_investors 100 300 200 1 1 NIL HORIZONTAL SLIDER 21 131 193 164 portion_passives portion_passives 0.1 0.9 0.5 0.05 1 NIL HORIZONTAL SWITCH 21 220 157 253 show-liquidity? show-liquidity? 0 1 -1000 MONITOR 20 284 106 329 Bank deposit deposit-bank 2 1 11 PLOT 675 16 967 166 Bank activity Time Liquidity 0.0 10.0 0.0 10.0 true true PENS "deposit-bank" 1.0 0 -16777216 true "loan" 1.0 2 -2674135 true MONITOR 21 342 78 387 Loan loan 2 1 11 MONITOR 23 400 124 445 NIL default-probability 4 1 11 MONITOR 678 371 802 416 NIL number-of-informed 17 1 11 PLOT 676 189 876 339 information diffusion time Number of informed 0.0 1.0 0.0 1.0 true false PENS "default" 0.1 0 -16777216 true SLIDER 21 173 190 206 financing-percentage financing-percentage 0.1 0.5 0.5 0.05 1 NIL HORIZONTAL @#$#@#$#@ WHAT IS IT? ----------- The model represents a simple financial market where investors interact with the banking system and they can both deposit and draw money. In the model there is also a company that receives funds from the bank and it can default with a low probability. The term "bank run" (also known as a run on the bank) refers to a situation in which a large number of bank customers draw their deposits because they believe the bank is, or might become, insolvent. HOW IT WORKS ------------ The bank in the model is represented by a group of yellow patches located in the centre of the world while investors and company are represented by turtles. The bank is an intermediate between the investors (subjects in financial surplus) and the company (subject in financial deficit). Investors are identical subjects and risk adverse with an initial unitary capital that they deposit in the bank. Even if identical, investors are divided in two categories: - passives (green turtles), that deposit/draw money in the bank with low frequency; - actives (red turtles), that have frequently need of liquidity and execute operations of deposit and draw in continuous way. Investors move randomly inside the model and when they touch the yellow patches (bank), they can operate in two ways: - if their liquidity is equal to one, they deposit one; - if their liquidity is zero, they can choose if draw an unitary amount or not execute operations. The choice between these two behaviours depends on a different probability assigned to the two categories of investors. The company, every fixed slot, applies for a loan to the bank; the latter gives it the funding in proportion to the deposit raised. The company can fail randomly with a probability of 0,01%. Furthermore, if the level of bank the deposit goes down a fixed value (0,3 * number_of_investors), the bank requires the restitution of 30% of the total deposit increasing the probability of default of 0,001. When the company fails, the bank can't recover the financing granted and investors are further divided into informed (orange turtles) and not informed (blue turtles). The informed ones will go to the bank for drawing the unitary amount deposited reducing the bank liquidity. With the decrease of bank deposits, the news of the default spread among other turtles, that will go to the bank to require the restitution of the unitary amount deposited, causing the default of the bank. HOW TO USE IT ------------- Start the simulation by clicking "Setup". Then, after clicking "Go", the turtles start moving and interacting in the way explained above; they keep on doing so until the "Go" button remains pressed. Button: Setup The Setup button resets everything to the beginning values and creates turtles (investors and company) and patches (banking system). Button: Go If clicked, the model starts running. Slider: number_of_investors This slider allows you to choose the number of investors you would like to begin the simulation with in a range from 100 to 300. Slider: portion_passives This slider allows you to choose the portion of passive investors inside the model. The slider goes from 0.1 to 0.9. Slider: financing-percentage With it you can change the portion of funding granted to the company, calculated in percentage of the total bank deposit. This slider goes from 0.1 to 0.5. Switch: show-liquidity? This switch activates the possibility of viewing the liquidity amount of each investor. Monitor: Bank deposit This monitor shows the amount of deposit collected by the bank. Its initial value is 5 that represents the bank reserve. Monitor: Loan With it you can view the total amount of financing granted to the company. Monitor: default-probability This monitor shows the probability of the company default. Its initial value is equal to 0.01% and it raises of 0.001 whenever the bank deposit goes below 0.3 * number_of_investors. Monitor: number-of-informed With it you can view the number of informed investors about the company default. Plot: Bank activity This plot shows the trend of two variables at every tick: bank deposit and loan. Plot: information diffusion This plot describes the diffusion of information about the company default. THINGS TO NOTICE ---------------- In this model it's important to notice that the company default is a rare event; when the default happens, the bank run occurs only if the bank has granted the financing at the company. If default happens after 1000 ticks, the system realizes an equilibrium between the amount of deposit collected and funding granted. After the company default, the news of the default rapidly spread but when the bank liquidity goes to 0 some investors remain not informed. THINGS TO TRY ------------- It's interesting to change the number of investors, the portion of passives and financing percentage to simulate different scenarios. EXTENDING THE MODEL ------------------- To improve the model we could introduce the company activity that depends on the amount of funding granted by the bank. The final product is bought by the investors of the model. In this way, when the bank requires the restitution of part of the financing granted, the company has further wealth derived from the sales. CREDITS AND REFERENCES ---------------------- F.C. Bagliano, G. Marotta, "Economia monetaria", ed. 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