PD forward looking model

1 Nội dung

Trong phần này thực hiện tính toán PD forward looking theo 3 kịch bản (base, upturn, downturn).

Các bước bao gồm:

• Chuyển đổi PD actual sang logit actual (PD ttc -> logit ttc)

\[ logit = log(\frac{p}{1-p})\]

• Hồi quy logit actual theo các biến vĩ mô

\[ \hat{logit}(p) = log(\frac{p}{1-p})= \alpha + \beta_1*MEF_1 + \beta_2*MEF_2 + ... + \beta_m*MEF_m \]

• Tính SE từ mô hình

\[ SE = \sqrt{\frac{SSE}{n-k}}\]

• Tính logit upturn và logit downturn

\[ logit_{upturn} = logit_{base} - SE\] \[ logit_{downturn} = logit_{base} + SE\]

• Tính pd upturn và pd downturn

\[ p_{upturn} = \frac{1}{1+e^{logit_{upturn}}}\] \[ p_{downturn} = \frac{1}{1+e^{logit_{downturn}}}\]

2 Thực hành

2.1 Đặc điểm dữ liệu

head(mef_data)

## # A tibble: 6 x 6
##   time                combank_foreign_~ cur_acct_bal_wma~ lending_rate_di~     d
##   <dttm>                          <dbl>             <dbl>            <dbl> <dbl>
## 1 2013-06-30 00:00:00              10.7            2.37              -1.6      0
## 2 2013-09-30 00:00:00              10.7            2.38              -1.5      0
## 3 2013-12-31 00:00:00              10.8            2.24              -1.47     0
## 4 2014-03-31 00:00:00              11.0            0.491             -2.35     0
## 5 2014-06-30 00:00:00              11.1            0.0031            -1.37     0
## 6 2014-09-30 00:00:00              11.1           -0.287             -1.27     0
## # ... with 1 more variable: actual_pd <dbl>

tail(mef_data)

## # A tibble: 6 x 6
##   time                combank_foreign_~ cur_acct_bal_wma~ lending_rate_di~     d
##   <dttm>                          <dbl>             <dbl>            <dbl> <dbl>
## 1 2023-09-30 00:00:00              24.0              3.08             -0.1     1
## 2 2023-12-31 00:00:00              24.2              3.22             -0.1     1
## 3 2024-03-31 00:00:00              24.4              3.63              0.2     1
## 4 2024-06-30 00:00:00              24.6              3.94              0.2     1
## 5 2024-09-30 00:00:00              24.9              4.14              0.2     1
## 6 2024-12-31 00:00:00              25.1              4.25              0.2     1
## # ... with 1 more variable: actual_pd <dbl>

Trong dữ liệu đã có sẵn các biến theo nhu cầu bao gồm: actual_pd, và các biến độc lập. Dữ liệu pd sau ngày 31/12/2018 chưa có sẽ được predict từ mô hình. Các bước tiếp theo chỉ cần thực hiện tính toán

2.2 Một số hàm cần thiết

#' @title Converse pd and logit
#' @param logit, pd  scalar or vector
#' @example fnc_logit_to_pd(fnc_pd_to_logit(-5.9))
fnc_logit_to_pd <- function(logit){
  to_pd <- 1/(1+exp(-logit))
  return(to_pd)
}


fnc_pd_to_logit <- function(p){
  to_logit <- log(p/(1-p))
  return(to_logit)
}

2.3 Tính toán

• Chuẩn bị dữ liệu

dt <- mef_data %>% 
  # create logit_base
  mutate(logit_base = fnc_pd_to_logit(actual_pd)) %>% 
  select(-time, -actual_pd)

• Hồi quy

m <- glm(logit_base~.,data = dt)

• Kết quả hồi quy

m

## 
## Call:  glm(formula = logit_base ~ ., data = dt)
## 
## Coefficients:
##                  (Intercept)      combank_foreign_liab_sma  
##                      -5.7758                        0.5524  
##       cur_acct_bal_wma_lead4  lending_rate_diff_yo_y_lead4  
##                       0.2669                        0.7019  
##                            d  
##                      -0.8732  
## 
## Degrees of Freedom: 22 Total (i.e. Null);  18 Residual
##   (24 observations deleted due to missingness)
## Null Deviance:       17.58 
## Residual Deviance: 3.548     AIC: 34.28

• SE

se <- m$deviance
se

## [1] 3.547727

• Tính pd upturn, pd downturn

out <- mef_data %>% 
  mutate(pred_logit = predict(m, newdata = mef_data)) %>% 
  mutate(logit_upturn = pred_logit - se,
         logit_downturn = pred_logit + se) %>% 
  mutate(pd_base = fnc_logit_to_pd(pred_logit),
         pd_upturn = fnc_logit_to_pd(logit_upturn),
         pd_downturn = fnc_logit_to_pd(logit_downturn))

res <- out %>% 
  select(time, pd_base, pd_upturn, pd_downturn)

res %>% 
  knitr::kable()

time	pd_base	pd_upturn	pd_downturn
2013-06-30	0.4156942	0.0200711	0.9611063
2013-09-30	0.4266553	0.0209748	0.9627527
2013-12-31	0.4440169	0.0224754	0.9652045
2014-03-31	0.2283355	0.0084470	0.9113308
2014-06-30	0.3565677	0.0157039	0.9506137
2014-09-30	0.3575732	0.0157717	0.9508189
2014-12-31	0.3309899	0.0140437	0.9450085
2015-03-31	0.4643924	0.0243541	0.9678621
2015-06-30	0.4774772	0.0256337	0.9694562
2015-09-30	0.5669555	0.0363236	0.9784831
2015-12-31	0.4910564	0.0270274	0.9710258
2016-03-31	0.3687396	0.0165390	0.9530283
2016-06-30	0.3006138	0.0122234	0.9372240
2016-09-30	0.3761971	0.0170661	0.9544361
2016-12-31	0.5228977	0.0305883	0.9744038
2017-03-31	0.4573544	0.0236901	0.9669693
2017-06-30	0.4937912	0.0273166	0.9713321
2017-09-30	0.5952843	0.0406260	0.9808023
2017-12-31	0.5596208	0.0352942	0.9778463
2018-03-31	0.7549408	0.0814665	0.9907411
2018-06-30	0.6968481	0.0620711	0.9876303
2018-09-30	0.8377509	0.1294152	0.9944551
2018-12-31	0.9007558	0.2071689	0.9968380
2019-03-31	0.8748386	0.1675221	0.9958980
2019-06-30	0.8712523	0.1630578	0.9957636
2019-09-30	0.8975897	0.2014911	0.9967260
2019-12-31	0.9016322	0.2087902	0.9968689
2020-03-31	0.8737379	0.1661300	0.9958568
2020-06-30	0.9347065	0.2918561	0.9979929
2020-09-30	0.9174640	0.2424401	0.9974167
2020-12-31	0.9625110	0.4250129	0.9988799
2021-03-31	0.9862549	0.6738180	0.9995989
2021-06-30	0.9937015	0.8195633	0.9998175
2021-09-30	0.9972651	0.9130285	0.9999211
2021-12-31	0.9976488	0.9243338	0.9999322
2022-03-31	0.9986756	0.9559655	0.9999618
2022-06-30	0.9989159	0.9636722	0.9999688
2022-09-30	0.9990914	0.9693791	0.9999738
2022-12-31	0.9992203	0.9736134	0.9999775
2023-03-31	0.9990725	0.9687604	0.9999733
2023-06-30	0.9992479	0.9745242	0.9999783
2023-09-30	0.9993670	0.9784726	0.9999818
2023-12-31	0.9994469	0.9811399	0.9999841
2024-03-31	0.9996454	0.9878289	0.9999898
2024-06-30	0.9997116	0.9900791	0.9999917
2024-09-30	0.9997589	0.9916931	0.9999931
2024-12-31	0.9997928	0.9928538	0.9999940