Credit Risk - An Agent-based Model of Post-credit Decision Actions and Credit Losses in Banks

7/31/2019 Credit Risk - An Agent-based Model of Post-credit Decision Actions and Credit Losses in Banks

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Credit risk:

an agent-based model of post-credit decision actions and credit losses in banks

Sara JonssonPh. D.

Centre for Banking and Finance,

School of Architecture and the Build Environment,

The Royal Institute of Technology KTH,

Drottning Kristinas vg 30,

100 44 Stockholm, Sweden

+ 46 8 790 86 68

E-mail: [email protected]


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Banks, however, differed in the extent to which they suffered from credit losses in this crisis.

Researchers and practitioners have offered various explanations for these differences. Some

have argued for bank-level governance explanations, such as poor incentive structures. For

example, some banks rewarded short-term performance rather than long-term performance,

thus influencing bankers to lend to high-risk firms and households. Some observers have

attributed the existence of poor incentive structures to lax oversight by boards and investors

that allowed bank management to develop such structures (Kirkpatrick, 2008). Others have

supported country-level explanations. For example, Beltratti and Stulz (2009) found that

banks in countries with stricter capital requirement regulations performed better during the

crisis.

Because of differences in corporate management and/or country regulations, bankers

exhibited different levels of risk aversion in credit decision processes and were thus exposed

to various degrees of risk as the crisis emerged. In this article, theterm credit decision process

refers to the decision that a banker makes as to whether to grant credit to a client. Theterm

post-credit decision process refers to the actions of a banker when clients are incorporated

into the banks credit portfolio. Although the factors that affect the credit decision process

have been previously investigated, the post-credit decision processhas receivedless attention.

Because a financial crisis can dramatically increase the credit risks of individual clients, post-

credit decision actions are of substantial importance. The aim of this study is therefore to

investigate the effects of individual bankers post-credit decision actions on bank credit

losses. The empirical setting constitutes bankers with permission to grant credit to firms.

The method involved the distribution of a survey to bankers and an agent-based model

(ABM). The survey provides information on the microfoundation of the banker agents, and


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the ABM is used to investigate the implications of an individual bankers actions on the risk

of the banks credit portfolio. Data on the firms were collected from a national database.

According to the findings presented in this paper, post-credit decision actions, particularly the

option to terminate contracts with risky clients, have a substantial impact on bank credit

losses.

2. BackgroundThe field of ABM in economics has developed considerably in recent years, resulting in the

application of ABMs in various economic environments (see Tesfatsion, 2003, for a review).

Included in these studies are the modelling of financial markets and organizations.

Financial markets are well organized and centralized and relative to markets for other goods,

they trade homogenous products in an efficient manner. As such, financial markets are

particularly suited for ABM (LeBaron, 2001). Among the numerous ABMs of financial

markets, the Santa Fe Institute Artificial Stock Market (SFI-ASM) (Arthur et al, 1997) is one

of the pioneering models. Other ABMs of stock markets include the work by Chen and Yeh

(2001), who constructed a stock market model that includes an additional social learning

mechanism. Foreign exchange markets have proved to be difficult to model with any

predictive power using conventional modelling approaches; however, they are suited for

ABM. Izumi and Ueda (2001), for example, constructed an ABM in which the agents

compete with each other to develop methods for predicting changes in future exchange rates.

Financial bubbles and crashes, or crises, in financial markets have received attention from

researchers and a number of ABMs have been proposed in this field. For example Brock and

Hommes (1998) present a model showing the bubble and crash dynamics when a majority of


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agents switch from a fundamentalist strategy to a trend-following strategy. Friedman and

Abraham (2009) later put forth a model of how bubbles and crashes arise from an endogenous

market risk premium that responds to investors recent losses.

Financial markets are composed of amorphous collections of agents. By contrast,

organizations have a formal structure and, commonly, an informal structure. The formal

structure serves to define lines of communication and distribution of decision making, and the

informal structure constitutes a channel for sharing information about mutual tasks. Whereas

ABM studies of financial markets investigate the effects of particular types of firm

behavioural rules on price dynamics and market structure, ABM studies of organizations

commonly focus on the effects of a firms organizational structure on the firms own resulting

behaviour (Prietula et al, 1998).

The neoclassical description of a firm is as a profit-maximizing entity. However, an agent-

based approach means not having to assign an objective to an organization. Instead, the agents

that comprise it are modelled with explicit attention given to how decisions are made and how

the interactions of these decisions produce organizational output. A primary task for

organizations is to constantly search for routines that improve performance. The objective of

ABM in this field is to understand how firm performance is influenced by the way in which

parallel searches are carried out among multiple agents (i.e. managers of different

departments independently searching for new routines) (Burton and Obel, 1980). In some

ABMs of organizations, various units work separately on solving similar problem such as

selling a particular product line to consumers. In these models, activities map into

performance in similar ways (e.g. Chang and Harrington, 2003). Other ABMs of

organizations, which are based on the assumption that different departments (e.g. sales,


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finance) solving different problems, investigate the interdependencies of conflicting needs

(e.g. Siggelkow and Levinthal, 2003). Another line of ABM of organizations investigates the

evolution of organizational structures (Ethiraj and Levinthal, 2002). Research has also

recognized the cost of processing information, which has been explicitly modelled in some

ABMs of organizations (Carley, 1992; Miller, 2001).

Although the application of ABMs has increased in studies of financial markets and

organizations, limited application exists infinancial organizations. Research in which ABM

has been employed to investigate financial risks and crises has studied the implications of

agent action in amorphous markets. However, ABM research is limited on the implications of

agent actions within an organizational structure and their effects on credit risk. The present

study puts forward a model of credit risk in banks and, as such, suggests a new area of

application for ABMs that is of value to both bank management and regulators. For example,

an ABM could serve as a complement to internal ratings-based risk (IRB) models in

estimating credit risk.

3. Data CollectionThe model presented in this paper, hereafter referred to as the Bank Model, involves banker

agents who have permission to grant credit to firms. The agents are modelled according to the

results of a survey investigation conducted in 2007 at one of the largest Swedish banks,

hereafter referred to as the Bank. The data collection was carried out by Volterra

(www.volterra.co.uk), a consultancy agency. The survey was sent to 470 bankers who have

permission to grant credit to firms. Of these 470 bankers, 321 answered the survey, yielding a

response rate of 68%. A copy of the survey is presented in Appendix 1. In addition, data were

collected from interviews with the management of the Banks credit risk department.


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4. Description of the Bank ModelThe Bank Model comprises a formal organizational structure (including the local banker

agents, the regional offices and the central office), an informal organizational structure and

the firms that constitute potential bank clients. These elements are addressed in the following

subsections.

4.1. The formal organizational structure

The Banks formal organizational structure consists of 1 central office, 8 regional offices and

455 local offices. The Banks policy is that clients should be assigned the bank office that is

closest to them. Geographical distance is therefore a parameter in the Bank Model. The

Banks formal organizational structure is geographically represented by a circular space in the

Bank Model (see Figure 1). The circular space is sliced into eight sections, with each section

representing a regional office. On each of the eight sections of the circumference, 455 local

bankers (each representing a local office) are located by randomly attributing an angle

between 0 and 360 to them, which determines the position on the circumference. In the

middle of the circle is the central office, to which all regional offices and local bankers are

connected. Figure 1 also shows how the space is used to distribute firms (potential bank

clients) across regions.

Insert Figure 1 about here

The three formal organizational levelsthe local bankers, the regional offices and the central

officeare described in the following sub-subsections.

4.1.1. Local banker agents


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This sub-subsection describes the goal, actions, cognitive limitations, learning process and

attributes (Table 1) of local banker agents.

Local bankers goal

According to interviews the employees at the Bank make a career based primarily on how

well they have avoided credit losses. Therefore, in the Bank Model, all local bankers are

assigned the same goal: to avoid credit losses.

Local bankers actions

The Bank is highly decentralized, meaning that credit decision authority and responsibility are

assigned to the local bankers. Analogously, in the Bank Model, the local bankers are the main

actors, in the sense that these individuals are the ones who do the following:

Decide whether to grant credit to firms that apply to them Make post-credit decisions by carrying out appropriate post-credit decision actions

from a list of possible oneswhenever a firms credit risk exceeds the allowed levels

As a general rule, each local banker grants credit to a firm provided that the following is met:

The perceived credit risk is below a certain limit set by the management. The size of credit being applied for is below the specific regional limit to which all

bankers in the same region are bound.

Local bankers limited cognitive abilities


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86%, the banker agent would also use other data from the client as a source of information

and so forth until all options were considered. The set of activities was then translated by

summing the usefulness indexes of the information sources (i.e. 0.41 + 0.30).



A high usefulness index is then translated to a low standard deviation. Hence, the range of

errors that banker agents make is narrowed if the source has been identified as being

important in the survey.

Local bankers learning process

Local bankers are assumed to have an individual, experience-based learning process.

Accordingly, as local bankers become familiar with the firms in their portfolios, they learn

more about their clients. This enhanced knowledge thus increases the accuracy of the bankers

assessments of the firms (cf. McNamara and Bromiley, 1997). Therefore, the error in credit

risk assessments is assumed to decrease in each time period, t, according to the following

negatively autocorrelated process (j denotes thej-th firm):

+ , (2)

where is the autocorrelation coefficient, and is the random component of the evolution

of the error term. When a firm that is already a client of the local banker applies for additional

credit, the local bankers current error term for that firm is retrieved and used in the evaluation

of the firm.

Insert Table 1 about here

4.1.2. The regional and central offices


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The main purpose of the regional and the central office in the Bank Model is to supervise the

credit application process for which the local bankers in the region are responsible. If the PPD

is below the PPD limit, but the credit size is above the local bankers credit limit, the regional

office handles the case by re-evaluating the applicant. The effects of this re-evaluation were

modelled according to survey results. Respondents were asked about the usefulness of

contacting the regional office and the central office in the evaluation of a credit application;

3% stated that the regional office was a useful source, and 1% stated that the central office

was a useful source. Correspondingly, in the Bank Model, if the regional office is contacted, it

is assumed that the local bankers usefulness index increases by 0.03 according to the survey

results; hence, the standard deviation of the error term decreases. If the credit size exceeds

even the regional offices credit limit, the local banker will also seek credit approval from the

central office. In this case, the usefulness index increases by an additional 0.01, and the

standard deviation of the error term decreases accordingly. However, according to

information obtained from the Bank, only 12% of the credit applications exceeded the local

bankers credit limits, and only 1% exceeded the regional office limit. If the loan size conveys

the involvement of the regional and possibly the central office and the firm is a previous

client, the local banker will use the error that is the smallest of the current stored error for that

firm (according to the local bankers learning process) and the error induced from the reduced

standard deviation.

4.2. The informal organizational structure

In addition to the formal structure, the Bank Model comprises an informal structure, which

means that local bankers can communicate with other local bankers in their region. When

banker agents are initialized, the local bankers are each assigned a random number (from zero

to the number of bankers in the region) of other local banker agents to be included in their


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network. According to the survey results, about 6% of the local bankers contacted other

branches in their region when they were making their last credit-granting decision. Thus, in

the Bank Model, 6% of the local bankers who handle a credit application use their informal

contacts. It is assumed that their clients have PPD values that are closest to the PPDLimit.

Hence, in each time period, the firms are sorted according to their PPD. First, the banker of

the firm closest to PPDlimit is identified, followed by the banker of the firm that is second

closest to PPDlimit and so on. This sorting process continues until 6% of the local bankers are

identified. The informal network is assumed to convey social learning, meaning that agents

are taught by other agents. Thus, in the model, the local bankers who use their informal

contacts assumed the same errorStd as the local banker of their informal contacts who has the

smallest errorStd.

4.3. The firms

In the Bank Model, firms constitute potential bank clients (see Table 2 for a list of firm

attributes). A firm is an instance of the firm class whose attributes are listed in Table 2.

Similar to banker agents, firms are assigned an angle on a circular space, which represents

their geographical location. When applying for credit, the firms address the banker that is

closest to them on the circle.

To assess the credit risk of publicly owned firms, lenders can use stock market prices. A

commonly used stock market-based credit measure is the expected default frequency (EDF)

model of Moodys KMV (1995). Because the Bank uses a version of this model to estimate

the credit risk of firm clients, it is also used in the Bank Model to model the firms. In this

model, the firms equity is valued as a call option on the firms underlying assets, which

implies that the firms equity holders have the option to repay the firms debts. When the


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firms debts mature, the firms equity holders can exercise their right to buy the firms assets

or choose to bankrupt the firm if the assets fall short of the debts. In three steps, the model

estimates a firms PD during a certain time period. The first step involves estimating the

market value of the firms assets (Vj), the volatility of the asset value ( )and the value of the

firms liabilities ( ).

In the second step, the firms default point and distance to default (DD) are calculated. The

default risk of a firm increases as the value of assets approaches the book values of the

liabilities until the firm finally reaches the default pointthat is, when the market value of the

assets is insufficient to repay the liabilities. In the model used in the Bank Model, the default

point is equal to Fj. In general, firms do not default when their asset values reach the book

value of debts because the long-term nature of some of their liabilities provides some

breathing space. The default point generally lies somewhere between total liability and short-

term liabilities (Crosbie and Bohn, 2003).

The distance to default ( ), which is calculated according to equation 3, is the number of

standard deviations that the asset value must drop so as to reach the default point. Hence, the

higher the risk of the firm the shorter the distance to default.

(3)

In the third step, an empirical mapping is constructed between the distance to default and the

default rate, based upon historical default experiences of firms with different DD values.

However, such data were not available. Therefore, the Bank Model approximates the


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probability distribution of the firms asset values as a normal distribution, with a mean equal

to and a standard deviation equal to . Hence, is estimated accordingly:

, (4)

whereNis the cumulative probability distribution function.

Each firm is also assigned an expected return on assets ( ) that is generated from a normal

distribution, with a mean of 0.04 and a standard deviation of 0.02, according to information

from the Bank. The expected return on assets is used when updating the PD in the simulation.

Figure 4 shows the distribution of the firms initial PD values generated by the Bank Model.

These values ranged from 0 to approximately 0.45.



5. SimulationThe model was built with a library-oriented approach (cf. Macal and North, 2010), using the

Java agent-based simulation (JAS) library (Sonnessa, 2004). The attributes of the Bank Model

are presented in Table 3. A description of the event schedule is presented in Table 4.



Firms applying for credit

In every time period, a random number of firms in the universe of firms apply for credit. A

credit is an instance of the Credit-class; the attributes of which are listed in Table 5.


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If a firm applying for credit is not a previous client of the bank, this firm is assigned to the

closest local banker.

Local bankers credit decision actions

In every time period, each local banker to whom a firm has approached with a credit

application makes assessments of the firms PD; hence, the PPD is calculated. If a firm

applying for credit is already in the local bankers credit book, the local bankers current error

term for that firm will be retrieved. If a firm applying for credit is not a previous client, an

error term will be drawn from the local bankers error distribution.

If the PPD is above the PPD limit, the credit application is rejected. If the PPD is below the

PPD limit, and the credit size is below the bankers credit limit, the local banker makes an

offer to the firm.

If the PPD is below PPD limit, but the credit size is above the bankers credit limit, the local

banker sends the application to the regional office, where the PPD is recalculated according to

the new usefulness index and the new standard deviation of the error term. If the new PPD is

above the PPD limit, the local banker declines the firms credit application. If the new PPD is

below the PPD limit, and the credit size is below the regional credit limit, the local banker

makes an offer to the firm. If the credit size is above the regional credit limit, the local banker

contacts the central office, where the PPD is recalculated according to a new usefulness index

and a new standard deviation of the error term. If this PPD is below the PPD limit, the local

banker makes an offer to the firm; otherwise, the local banker declines the firms credit

application.


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Local bankers post-credit decision actions

The PDs, and thus the PPDs, of bank client firms changes for each time period potentially

causing an excess of the PPD limit. In the survey, bankers were asked what type of action

might be carried out if a client firms PPD exceeds the PPD limit. The survey results were

transferred to available model actions (Table 6).


Accordingly, three different post-credit decision actions are modelled in the Bank Model. All

bankers adopt the same option in the same situation. These three options are compared so as

to estimate the impact of post-credit decision behaviour.

1. No actions are carried out when a firms PPD exceeds the PPDlimit.2. When the PPD exceeds the PPDlimit, exposure to the client is halved; however, the

firm is still a customer of the bank.

3. The bank will terminate its contract with any firm with a PPD that exceeds thePPDlimit. In accordance with information obtained from the Bank regarding contract

termination, a credit loss of 20% of the firms book value of liabilities (F) is assumed.

Update of firms PD

At every time period, t, the PD of all firms is recalculated according to its actual return (rj)

and expected return (j). rj of each firm evolves according to the following:

, (5)


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where ej is a firm-specific shock. The firm-specific shock is introduced at every time

period, t, and is drawn from a normal distribution, with a mean of 0 and a variance equal to

the volatility of the firms asset value. Each firm is allocated a goodness-of-fit measure, ,

from 0 to 1. A new net asset value (the numerator in equation 2) for each firm is calculated

using the values of rj, j, and the current contractual liabilities ( ):

exp (6)

The equation can be described as a fractal Brownian motion, where tis the current time

period,fis the frequency of change in asset value (annual: f = 1, monthly: f = 12, etc.). In the

results presented in this paper, an annual frequency of change is assumed. The Hurst

parameter,H, allows for the return process to be autocorrelated. IfHis equal to 0.5, there is

no autocorrelation; ifHis more than 0.5, there is a positive autocorrelation; and ifHis less

than 0.5, there is a negative autocorrelation. In the Bank Model,His randomly assigned from

a uniform distribution ranging from 0 to 1. Using the new net asset value a new PD is

calculated.

In this step firms with a DD value of 0 are identified. These firms are considered defaulted

firms and are replaced with new firms. Hence, number of firms that can apply for credit is

assumed to be constant.

Calculation of credit losses

At each time period, a certain number of firms will reach their default point and the bank will

incur a credit loss if the firm is a bank client. The loss given default (LGD) is a measure of the


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Figure 8 shows the means of the simulation results for all three post-credit decision action

options at PPD limit values ranging from 0.01 to 0.45 (cf. the distribution of PD values

illustrated in Figure 4).Each point in the figure represents the mean losses from t= 0 to t=

300. The means and standard deviations of each point are presented in Table 7



For all three options, the bank is assigned an equivalent PPD limit that represents equal risk

aversion. As previously mentioned, one type of asset is assumed; hence, the differences at

each PPD limit are not dependent on the composition of the banks credit portfolio.

The results show that the post-credit decision actions have a substantial effect on bank credit

losses. When bankers half the exposure to clients where PPD exceeds the PPD limit (option 2)

losses are reduced. The results further show that option 3 (terminate contracts with all clients

whose PPD exceed the limit) has the greatest impact on reducing bank credit losses. For

example, a PPD limit of 0.01 in option 1 approximately corresponds to a PPD limit of 0.20 in

option 3, in terms of the proportion of the credit losses.

Figure 8 shows that under option 1 (no post-credit decision actions carried out), the degree of

risk aversion has a substantial effect on credit losses that are already at low PPD limit values.


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By contrast, under option 3 (termination of contracts), risk aversion begins to exhibit

substantial effects on credit losses at PPD limit values above approximately 0.2.

Option 2 (exposure halved to clients whose PPD value exceeds the PPD limit) approximates a

linear relationship between the PPD limit and expected credit losses. In the Bank Model, this

option does not incur extra losses but still results in higher credit losses than option 3.

However, as the PPD limit increases, the proportion of credit losses approaches that of option

3. Hence, if a firm should suddenly convey a high PPD value (e.g., caused by a shock), the

option to halve the exposure might be considered above terminating the contract because the

former action would allow the bank to keep a customer who could potentially recover and

remain a profitable client.

The variables in the Bank Model were populated using empirical data obtained from a survey

distributed to local bankers at the Bank and using information obtained from interviews with

the management team of the Banks credit risk department. In this way, the agents actions,

attributes and input value ranges are validated. Furthermore, the firm clients were

operationalized using data from a database (www.largestcompanies.com) that provides

information on the asset values of Swedish firms. Additional input values on the firm clients

were obtained from the Bank.

The model output shows the impact of post-credit decision making on the extent of credit

losses (i.e. through decreasing exposure or terminating contracts with clients when the PPD

exceeds the PPD limit). These actions require early detection of credit deterioration and

actors speedy decision making. If a firm has multiple banks, it is potentially easier to make

the firm leave if one of these banks is the first to recognize the deterioration of a client. If one


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of these banks is instead the last one to recognise the firms deterioration, the firm might feel

that it has no other option than to stay with the bank even though interest rates and demands

for collateral are raised. Bankers post-credit decision are made in an environment that is

characterized by great uncertainty. In such environments organizations benefit from

decentralising decision making because decentralisation promote responsiveness to markets

(Lawrence and Lorsch, 1967).

The Bank has a history of decentralizing credit decision and post credit decision authority.

Hence, the Bank has an organizational structure that is favourable to early access to

information about clients as well as speedy action. Further, credit loss data obtained from the

Swedish banks annual reports (1998-2010) show that the Bank has suffered lower credit

losses than other Swedish banks (see Figure 9).


Conclusion and discussion

The ABM presented in this paper simulates the impact of bankers post-credit decision actions

on bank credit losses. The main analytical result is that post-credit decision actions have a

substantial impact on banks credit losses and credit risks. The results show that terminating

contracts with high risk client has the highest impact on reducing credit losses, followed by

the option to halve the exposure to risky clients. In the validation discussion it is suggested

that a decentralized organizational structure is beneficial to the possibility of terminating

contracts.


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Besides the suggested impact of a decentralized organizational structure to the possibility of

terminating contracts the different post-credit decision action options might have motivational

explanations. Agents have preferences (i.e. agents like financial rewards and career progress).

How preferences translate into behaviour depends on an organizations incentive scheme for

rewards and punishment (Chang and Harrington, 2006). Most organizations strive for

profitability (e.g., Cyert and March, 1963), which creates pressure for profitability at the

operating level (Bower, 1970). The profitability goals of bank organizations may be translated

into credit growth targets at the operating level. Because profitability rises with increases in

both sales of credits and services to clients, growth in credit portfolios is a way to improve

performance (McNamara and Bromiley, 1997). If pressure for growth in credit portfolios is

combined with an organizational setting where acknowledgement of a poor decision results in

undesirable outcomes (e.g., the threat of increased oversight, reduced responsibility or loss of

rewards), bankers might refuse to acknowledge the deterioration of a borrowers condition.

Undesirable outcomes might even result in an escalation of commitment, which implies that

banks may either increase or maintain credit lines for borrowers, despite their deteriorating

financial positions (McNamara et al, 2002). Neglecting to carry out post-credit decision

actions (option 1) may illustrate the behavioural outcome of such motivational settings.

If a bank rewards bankers for avoiding losses (i.e.bankers with a record of the lowest losses

have the best career opportunities at the bank) and provides an organizational setting in which

the deterioration of a creditor does not result in undesirable consequences bankers are more

likely to behave by terminating a contract with a client whose PPD value exceeds the PPD

limit value (option 3).


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The present study answers the call for a greater focus on the needs of practitioners in ABM

(Siebers et al, 2010) because it provides implications for both banks and regulators. The

results provide implications for regulators to take into account banks post-credit decision

actions when imposing capital requirements as a complement to the focus on bank assets. For

banks, an ABM could be used as a potential tool in the IRB approach. The Basel framework

encourages banks to initiate an IRB approach when measuring credit risk because banks are

expected to be capable of adopting sophisticated techniques in credit risk management. In

accordance with this approach, banks are allowed to develop their own credit risk models.

To increase the validity of the model, survey results should be collected from multiple banks.

Future models should also explicitly investigate the impact of bankers motivations (i.e.

rewards or individual preferences) to their post-credit decision actions.

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Table 1 Local banker attributes

Local banker Attributes Comment

angle The local bankers are each assigned a unique random angle between 0 and 360, which represents their

geographical location.

yearsToRetirement According survey results, the bankers have been working at the bank for a mean period of 10 years (SD = 4years). From this distribution, N (10, 16), the banker agents are assigned a certain number of years that they

will work in the bank.errorMean All banker agents are assigned an individual error distribution. All distributions, however, have the same

mean (0).

errorStd The bankers are assigned a different standard deviation of the error term.

minRho The minimum possible value for the autocorrelated component of the error (70%)maxRho The maximum possible value for the autocorrelated component of the error (90%)

minEta The minimum possible value for the random change of the error in any time period (2%)maxEta The maximum possible value for the random change of the error in any time period (2%)

localPortfolio The local bankers client firms are recorded in a list (localPortfolio). Each firm is associated with a specificerror term.

CreditLimit Data on the credit limits were obtained from the survey. Regional credit limits ranged from 1 239 474 SEK

to 15 000 000 SEK. These limits are distributed to the local bankers, according to region. All local bankerswithin the same region are assigned the same credit limit.

PPDLimit The expected credit losses are calculated for various limits for perceived probability of default, PPD,

ranging from PPD = 0.01 to PPD = 0.45.informalContacts The local bankers are assigned a network of other local bankers, who constitute the local bankers informal

contacts. The informal contacts are recorded in a list (informalContacts).

Table 2 Firm attributes

Firm Attribute Comment

firmAngle Firms are assigned a unique random angle between 0 and 360, which represented their geographical location.

assetValue Information (www.largestcompanies.com) on total asset values was obtained from 26 532 public and private

businesses. The total sample size was limited to 20 841 firms with asset values below 100 million Swedish kronor(MSEK). The data were fitted by an exponential distribution, with a mean equal to 15 MSEK. The market asset

value of a firm in the Bank Model was randomly assigned from this exponential distribution.

volatility Volatility is a measure of the standard deviation of the annual percentage change in asset value, which is a

measure of a firms business and industry risk. The annual volatility was derived from a uniform distribution witha range from 0.3 to 0.5, according to information from the Bank. Firms with larger asset values are assigned lowervolatility.

leverageRatioAccording to the Banks estimates of client firms proportion of debt to asset values, firms leverage ratios ( )

in the Bank Model are randomly generated from a uniform distribution with a range from 0.2 to 0.9,

corresponding to a leverage of 20 to 90%. The leverage ratio is used to calculate the contractual liabilities, = V

j .

expROA The expected return on assets is generated from a normal distribution N(0.04, 0.0004)

bankLoans List containing the credits obtained from the Bank

Table 3 Bank Model attributes

Bank Model attributes Comment

numberOfLocalBankers 455

numberOfRegions 8numberOfCentralOffices 1

Expected CreditLoss Calculated each time period

Time Time is set to 300PostCreditDecisionOption Three options are available to the local banker: (1) noAction, (2) exposureHalved or (3)

terminateContract.

numberOfFirms 2000

Table 4 The Bank Model event schedule


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Step Event

Step 1 Initialization {

Generate the initial population of local bankers, the banks formal and informal structure and the firms.}

Step 2 Firms apply for credit {Randomly select n (between 0 and numberOfFirms) firms that apply for credit

For each firm that applies: If the firm is not a previous customer, assign the firm to the closest banker}

Step 3 Local bankers make the credit decisions {From the list of firms that apply for credit, if PPD < PPDLimit, grant credit}

}Step 4 Local bankers make post-credit decisions {

If option = 1, go to step 5

If option = 2, for client firms with PPD > PPDLimit,

halve the credit exposureIf option = 3, for client firms with PPD > PPDLimit,

terminate contract (remove the firm from the local bankers credit book)

}Step 5 Update firms PD {

For each firm in the universe of firms, calculate a new PD

}Step 6 Calculate credit losses {

For each client firm whose DD = PPDLimit, calculate loss (0.20 *debt level (F))}

Step 7 Replace defaulted firms {

Create n new firms equal to the number of defaulted firms}

Step8 Replace retired bankers {

For each local banker, if yearsInBank = yearsToRetirement, replace the local banker with a new bankerStep 9 update banker error term {

according to the local bankers learning process

}

If t < time, go to step 2.

End.

Table 5 Attributes of the Credit class

Credit Attribute CommentcreditID The credit identification number

creditSize The size of the credit is drawn from a uniform distribution with a

range from * 0.05 to * 1.00.

creditMaturity The credits are assigned a certain maturity, according to information

from the bank. There is a 10% probability that the credit will matureand be repaid after 2 years. There is a 63% probability that it is

repaid after 4 years, and a 27% probability after 8 years.

creditAge The age of the credit increases by 1 for each time period.

Table 6 Transfer of results for the question regarding available post-credit decision actions to

Model action

Intervention options as stated in the survey Model actionNo actions are taken No action

Measures to facilitate for the client (e.g., extended credit) Exposure is halved, but the client is still a bank customer.

Measures to reduce the risk of loss

Measures to reduce future exposure to the customer

Measures to phase out the relationship

Measures to terminate all credits to customer (For example byraising the interest rate or collateral to levels that will make the firm

voluntarily leave the bank. )

The client is removed from the bank.


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Table 7 Mean and standard deviation of expected credit losses at various PPD limits

PPDLimit 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Option 1

Mean 0.002 0.021 0.033 0.034 0.036 0.039 0.039 0.040 0.042 0.043

SD 0.002 0.001 0.004 0.002 0.003 0.004 0.002 0.002 0.003 0.006

Option 2

Mean 0.000 0.005 0.010 0.013 0.016 0.022 0.025 0.033 0.035 0.037SD 0.000 0.000 0.001 0.002 0.001 0.002 0.003 0.004 0.004 0.004

Option 3

Mean 0.000 0.000 0.000 0.001 0.003 0.016 0.024 0.027 0.033 0.035

SD 0.001 0.000 0.000 0.000 0.000 0.002 0.003 0.002 0.004 0.004

Note: Number of runs = 10.


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Figure 1 The formal structure of the Bank Model

Figure 2 Responses to questions about information sources used in their last credit-granting

decision

Figure 3 Responses to questions about the most useful information sources used in their last

credit-granting decision


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Figure 4 Distribution of initial probability of default (PD) values

Figure 5 Expected credit loss (percentage)when the bankers have the option to terminate the

contract with all firms in which the perceived probability of default (PPD) exceeds the PPD

limit of 0.10 (option 3).


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Figure 6 Expected credit loss (percentage)when the bankers have the option to halve

exposure to firms in which the perceived probability of default (PPD) exceeds the PPD limit

of 0.10 (option 2).

Figure 7 Expected credit loss (percentage)when the banker take no actions of firms in which

the perceived probability of default (PPD) exceeds the PPD limit of 0.10 (option 1).


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Figure 8 Simulation results from all three post-credit decision action options; mean of

expected credit losses as a percentage of the total borrowing at different limits for perceived

probability of default (PPD limits) .

Figure 9 Credit losses (percentage) of the Bank and other banks in the Swedish market, 1998-

2010.

Credit Risk - An Agent-based Model of Post-credit Decision Actions and Credit Losses in Banks

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