ࡱ> BDA5@ ]bjbj22 &`XXU6666<r?0:p"""///////$11R3/E"!^"""//$$$"/$"/$$$$:),^@f*. 0U6"X * +00?0*RC4I#`C4f*f*C4z*8""$"""""//6$6The transition of payment behavior for credit card users Framework DANDAN Huang 1 Objective This project will research on the transition of payment behaviors for credit card users. The system will enable the firm to develop controls on the issuance of credit cards which depend on the expected value and variance of the net revenue of the applicant. Customers will have many different payment behaviors. Many revolving credit accounts take advantage of the revolving credit option, but some prefer to pay the entire balance each month; yet others may remit the minimum required payment each month, using the credit card as a source of short-term funds. Therefore, dynamic analysis on the cycle of credit card is very important for us to understand the whole payment behavior of clients. Basically, we focus on three issues on credit card cycle system: a) Transition probabilities from one status to another status. b) Expected time an account will remain in a given state once it has entered it---- the sojourn time for that state. c) How much balance (BT balance and Protective balance) they have for each status Here, we have basic definitions for each status. FCPurch BalBalBT AmntLate FeeOL FeeInactive000000Transactor0++?00000Paydown+0000?0?0Revolver++0+00?0?0Closure000000 For the revolvers, balance will be divided into sub-segments. A current account with a small opening balance might be more likely to be paid off in the next period than an account with a large opening balance. That is, transition probability may be dependent on the size of the opening balance. To investigate whether a size-effect exists, the second state-splace definition subdivides the current state into five separate states:[11/3 markov chain approaches to the analysis of payment behavior of retail credit customers] Current account with an opening balance less than; Current account with an opening balance between At the start of any payment period an account could be classified into the following states: State 1: inactive account(opening balance less than 10) State 2: true revolver(total outstanding balance repaid within the period); ????? this is transactor State 3: Payment less than the total outstanding, but greater than the mrp; State 4: payment within 0.5 of the mrp State 5: payment less than the mrp(but still positive); State 6: no payment This is definition from that paper. 2 Methodologies Markov models have been successfully employed in various sciences for many years and their properties are well developed. A number of Markov Chain approaches will be developed. This approach allows the firm to analyze the payment behavior of its customers on a timely basis and can provide the foundation for future forecasts of payment behavior, and hence profits. Another advantage of using this approach is to develop a dynamic model instead of static model we use now. 3 Data In order to estimate the Markov Chain model, data on customer credit activity for 18 months are needed. Accounts in this dataset should be new at the beginning. It can help us to follow their payment behavior changes. 4 Schedules First Step:   In this step, Key variables statistics analysis and segments analysis will be done. Then, transition matrix will be developed according to stationary Markov chain model. Probability in transition matrix will be used in the regression model for individual accounts. Finally, we need to test the goodness of fit for the model. We randomly divided the time-aligned dataset into subsets for cross-validation. Each observation was assigned a random uniform value. Second step: Using Non-stationary Markov chains, seasonality problem will be solved. In this step, 24 months data need to be used. Third step: Move-stayer model will be applied in this step. Move-stayer model divide people into two segments: People never change their status & People switch their payment state during the period. Using this model, heterogeneity problem will be discussed in this step. Appendix: 1 Variable: Bureau DataDemographic DataEducationPotential incomeTime in jobProfessionNumber of dependentsHow many cards they haveAgeStatistics DataTime at bankOn-book DataBalanceFinancial ChargePurchase balanceBalance transfer amountLate feeOverlimit feeDelinquency timeRespond rateMinimum required paymentsActual payments 2 Markov Chain Model First, we assume that the stochastic process is stationary; therefore we use stationary Markov Chains,  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Here,  EMBED Equation.DSMT4  is the number of observations in state i.  EMBED Equation.DSMT4  is the number of observations in state k at time j which were in state i at time h;  EMBED Equation.DSMT4 is a summation of  EMBED Equation.DSMT4 over all time j. Therefore, we have a transition probability matrix. 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