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view/download model file: real_estate_and_interest_rate.nlogo
The model simulates the effects of changes in loan interest rates (3 mounth Euribor) on the number of mortgage loans allocated (fixed and floating interest rate), on the instalments' amount, on the borrowers' solvency and on the real estate value that constitutes the guaranty below the loan.
The agents (turtles with person shape) are composed by:
- persons blue: agents that rise a floating interest rate loan;
- persons green: agents that rise a fixed interest rate loan;
- persons white: agents blue or green that are unbankable according to their own features (monthly income, money, consumption and initial endowment);
- persons red: agents that become insolvent during the simulation.
The model takes inspiration from the recent facts of "sub-prime" that involved the US bank system in the last years.
Every loan required by the agent set is equal to the real estate value and the life of loan is directly proportional. The contracts' features (amount and duration) are the same for all the agents but they change during the simulation for the new borrowers according to real estate value variations.
The initial number of borrowers is inversely proportional (according to the level of beta choosen from the provided slider) to the relative variation between the initial interest rate and that of a previous year (both randomly generated). This number is then proportionally divided in floating borrowers (blue) and fixed borrowers (green): if interest rates go up, the majority (70%) will rise a fixed interest rate loan, while if interest rates go down, the majority (70%) will rise a floating interest rate loan.
This rule is the same during the simulation, in which the interest rate comparison is ever done between the initial interest rate and that just generated (Euribor).
The Euribor is generated as follows:
- with probability 1/2 the Euribor is equal to the sum of the last level generated and a random number between 0 and 0.3;
- with probability 1/2 the Euribor is equal to the difference of the last level generated and a random number between 0 and 0.3.
The fixed interest rate for the green agents is the first annual rate generated when they rise the contract, remaining constant until the time to maturity of the loan.
Both the interest rates are transformed into monthly rates to calculate the periodic instalments that borrowers have to pay (french amortization plan, constant instalments).
The features of each borrower are: monthly income, initial endowment proportional to the annual income, monthly consumption proportional to the monthly income, money available on the c/c, amount of loan, monthly instalment, capital and interest share of instalment and the relative quantities paid, residual debt, number of monthly instalment foreseen by the contract, number of instalments paid, total cost and possible amount of insolvency (difference between the loan's amount and the capital shares paid).
The agents that are unbankable change their color in white, move in the centre of the monitor and then disappear.
During the simulation, for every tick, the agents receive their montlhy income, pay the instalment and the consumptions. When they finish to pay their loan they disappear from the monitor. If the difference monthly income - consumption - monthly instalment is negative but the money on their c/c is congruous, they can use their liquidity as last possibility. And if also the money is not enough or it's already finished, the borrowers are insolvent. They become red and disappear from the monitor. The real estate mortgaged and then sold by the bank has a negative effect on the real estate value because the supply increases (the lost of value is equal to 100 € for each insolvent).
The real estate value is naturally linked to interest rates varations. If the interest rates go up, the demand of real estate go down and consequently its value. Viceversa, if the interest rates go down the real estate value increases.
The gain/lost of value is inversely proportional to the interest rate variations according to the level of beta choosen from the provided slider.
Every tick, if the level of Euribor goes down the maximum accettable level choosen from the provided slider, the model creates a number of new borrowers according to interest rates variations (inversely proportional) and real estate value variations (directly proportional) and the respective betas choosen from the provided sliders.
Moreover, if the real estate value go down the minimun desirable real estate value choosen from the provided slider, new agents will rise loans in despite of high levels of interest rate and this fact will increase the real estate value of 100 € each new borrower.
It's possible to separate the interest rate effect from the real estate value effect on the number of new borrowers and separate the interest rate effect from the insolvents effect on the real estate value from the provided switches.
The "Setup" button creates turtles (new borrowers divided into agents blue, green and white) and generates the initial interest rate and that of a previous year (the Euribor and the fixed annual rate are equal to initial interest rate).
Through the inputs "initial-debt" and "years" it's possible to choose the initial contract features. The slider "spread" allows to estabilish the spread applied by the bank. The user can also choose the range of annual income of the agent set from the chooser "min-income" and "max-income", the portion of annual income that constitutes the initial endowment for each agent from the slider "endowment/income" and the portion of monthly income that consitute the monthly consumption for each agent from the slider "consumption/monthly-income".
Three monitors allow to know each time which is the number of bank's customers, the number of floating borrowers (blue) and the number of fixed borrowers (green) present in the monitor. Other two monitors indicate for each time the number of new borrowers created ("new-borrowers") and the number of insolvents ("insolvent-customers").
The sliders "beta-interest/value", "beta-interest/n.borrowers" and "beta-value/n.borrowers" allow to determine respectively the entity of real estate value variation after an interest rate variation, the entity of number variation of new borrowers after an interest rate variation and the entity of number variation of new borrowers after a real estate value variation.
Through the slider "max-accettable-interest" it's possible to choose the maximum level of loan cost (not yet comprhensive of spread) that the agents can support and through the slider "min-desirable-real-estate-value" the minimum value at which the agents are disposed to purchase a real estate in despite of too high level of loan's interest rates.
The switches "add-real-estate-value-effect?" and "add-n.insolvents-effect?" allow respectively to add or not the effect on the number of new borrowers created each time due to changes in the real estate value or to the collapse of real estate value under the minimum desirable real estate value and to add or not the effect on the real estate value due to a number of insolvent borrowers.
There are four graphs that show some interesting relationships beetwen the pattern of interest rates, the pattern of real estate value, the entity and the composition of new borrowers during the time and the number of insolvent agents.
"Interest Rate" compares the level of Euribor and the level of interest rate underwrited by those who rise a fixed interest rate loan. When the two interest go toghether it means that new borrowers are created at each time. It's very interesting to try to understand which kind of borrowers has done the best choice (ex post).
"Real Estate" show the pattern of the value during the time and always compares it to the initial value and the minimum desirable value. Note that when the value go beyond the minimum desirable value (orange line) the level of Euribor is very high and, if the switch "add-real-estate-value-effect?" is on, anyway new borrowers are created.
"New Borrowers" points out the number of new borrowers created each time and its composition between floating borrowers (blue) and fixed borrowers (green).
"Insolvents" show the number of insolvent agents for each time.
Stop the simulation in a certain point and compare the level of interest rates with the number of new borrowers and the real estate value.
Are all the floating agents able to respect the loan? And if someone results insolvent, which is the entity of the insolvency and their own features? Who is able to pay all the variable instalments according to the level of income, consumption and money?
Is it true that, even if probably more convenient than a fixed interest rate loan, to respect a floating loan it should be better belonging to a middle-high income's segment?
It's also interesting compare the level of Euribor and the level of interest rate underwrited by those who rise a fixed interest rate loan. When the two interests go toghether, it means that new borrowers are created at each time. Try to understand which kind of borrowers has done the best choice.
Then, setting the speed at level slower, try to see in the features of those agents that have discharged the debt (and so, a little before they disappear from the monitor) how much they have paid at the voice "total cost" and compare it with the size of the debt (initial real estate value) and with the actual real estate value, to quantify the possible gain-lost of the investment.
The user can modify the value of the inputs, sliders and choosers relating to:
- the size of initial debt (that is equal to the initial real estate value);
- the years to discarghed the loan;
- the spread applied by the bank;
- the range of annual income of the agent set;
- th ratio initial-endowment/annual-income;
- the ratio consumption/monthly-income;
- the maximum level of Euribor accepted by the potential new borrowers;
- the minimum real estate value desired by the potential new borrowers that can drive them to purchase in despite of too high loan's cost;
- the entity of real estate value variation after an interest rate variation;
- the entity of number variation of new borrowers after an interest rate variation;
- the entity of number variation of new borrowers after a real estate value variation.
Moreover trough the switches "add-real-estate-value-effect?" and "add-n.insolvents-effect?" it's possible respectively to add or not the effect on the number of new borrowers created each time due to changes in the real estate value or to the collapse of real estate value under the minimum desirable real estate value and to add or not the effect on the real estate value due to a number of insolvent borrowers.
We have considered as costants trough the time features like income and consumption.
To improve the model we could introduce the changes in these variables due to the interest rates pattern and prices. It could simulate a simplified economy in recession or in expansion.
The simulation is based on :
- Terna P., Boero R., Morini M., Sonnessa M. "Modelli per la complessità. La simulazione ad agenti in economia". Ed. Il Mulino 2006. http://abm.econ.unito.it/.
- Ian Stewart "Langolo matematico", Le Scienza n. 313, settembre 1994.
- Domenico Parisi "Mente come Cervello", Le Scienze n. 431, luglio 2004.
- Pietro Terna e Riccardo Taormina "Modelli di simulazione con agenti intelligenti: il sorprendente mondo dei camaleonti".