Workout LGD: the reference data set from default events and cash flows

Builds the reference data set (RDS) of realized loss given default, one row per default event, from a table of default events and the long table of their post-default cash flows. Every cash flow is discounted to the default date at the reference rate in force at that date plus lgd_discount_add_on, with monthly compounding over whole months: $$\mathrm{PV} = \frac{A}{(1 + r/12)^{t}}$$ where t is the number of whole months between the default date and the cash-flow date. The realized LGD is the economic loss $$\mathrm{LGD} = \frac{E - \mathrm{PV}(R) + \mathrm{PV}(C) + \mathrm{PV}(D) + C^{\mathrm{ind}}}{E}$$ with E the exposure at default, R recoveries, C direct costs, D drawings after default and C^ind the indirect costs allocated by lgd_cost_allocation.

Usage

scr_workout(
  defaults,
  cashflows,
  rates = NULL,
  config = scr_config(),
  indirect_costs = 0,
  obs_date = NULL,
  keep_rows = FALSE
)

Arguments

defaults: A data.frame or data.table with one row per default event: default_id, facility_id, default_date, ead, product, status ("closed", "cured" or "open"), optionally close_date, plus any driver columns, which are carried into the RDS.
cashflows: Long table: default_id, date, amount, type ("recovery", "direct_cost" or "drawing").
rates: Optional table (date, rate) of the annual reference rate; the rate in force at the default date is used. NULL uses the flat lgd_discount_rate of the configuration.
config: A scr_config(); keys lgd_*.
indirect_costs: Total indirect workout cost to allocate: a single number, or a table (product, amount) allocated within product.
obs_date: Observation date; NULL uses the latest date seen.
keep_rows: Keep the cash-flow table with its present values.

Value

An object of class scr_workout: rds (one row per default event: identifiers, default_date, ead, product, drivers, status, months_in_default, discount_rate, pv_recovery, pv_cost, pv_drawing, cost_indirect, recovery_extrapolated, lgd_raw, lgd_real, is_cure, is_incomplete, merged_n), recovery_profile (product x month: cum_recovery), extrapolation (per open event), funnel (rule, n, action), summary (n, cure_rate, lra_default_weighted, lra_exposure_weighted, share_incomplete, discount_rate_mean, by_product, by_year), ledger, config, obs_date, and cashflows with keep_rows. rds also carries year, close_date, recovery_nominal, recovery_artificial, cost_nominal, drawing_nominal, closed_at_t_max, absorbed, n_cashflows and last_month; funnel has kept; summary has n_cure, lra_raw, ead_total and years.

Rules

Cures. An event with status == "cured" returns to performing: the balance outstanding at the cure date (ead plus the drawings after default, net of the cash recovered) enters as an artificial recovery on the cure date, so the cure carries its costs and the discount effect, never a zero loss by decree.
Multiple defaults. Two defaults of one facility separated by fewer than lgd_cure_window months (from the close of the first to the start of the second), or a new default while the first is still open, are one event: the first default date and exposure are kept, the cash flows of both spells are pooled and the status of the last spell rules.
Incomplete workouts. An open event younger than lgd_t_max months receives the expected further recovery read from the recovery profile of the closed defaults of the same product (cumulative discounted recovery rate by month in default); an open event at or beyond lgd_t_max is treated as closed with no further recovery.
Bounds. With lgd_floor_at_zero the realized LGD used in the averages is floored at zero and with lgd_cap_at_one capped at one; lgd_raw always keeps the unbounded value.

The long-run average is reported default-weighted (the arithmetic mean over events) and exposure-weighted, overall, by product and by calendar year of default.

Examples

cfg <- scr_config(verbose = FALSE)
wo <- scr_workout(scr_demo_lgd, scr_demo_lgd_cashflows, rates = scr_demo_rates, config = cfg)
wo
#> <scr_workout> 885 default events | 8 calendar years | observation date 2026-06-28
#>   cure rate 37.5% | incomplete 18.1% | mean discount rate 14.37%
#>   long-run average LGD: 40.5% default-weighted | 29.9% exposure-weighted | raw mean 40.5%
#>   auto         n 203   cure 36.5%   LRA 34.4%   (ew 35.9%)
#>   mortgage     n 237   cure 46.8%   LRA 26.3%   (ew 26.7%)
#>   unsecured    n 445   cure 33.0%   LRA 50.8%   (ew 51.3%)
#>   funnel MULTIPLE_DEFAULT_MERGED      15
#>   funnel OPEN_BEYOND_T_MAX_CLOSED     2
#>   funnel INCOMPLETE_EXTRAPOLATED      160
#>   funnel LGD_ABOVE_ONE                3
wo$funnel
#>                        rule     n
#>                      <char> <int>
#> 1:             NOT_IN_SCOPE     0
#> 2:  MULTIPLE_DEFAULT_MERGED    15
#> 3: CASHFLOW_WITHOUT_DEFAULT     0
#> 4: OPEN_BEYOND_T_MAX_CLOSED     2
#> 5:  INCOMPLETE_EXTRAPOLATED   160
#> 6:     NEGATIVE_LGD_FLOORED     0
#> 7:            LGD_ABOVE_ONE     3
#>                                                                                        action
#>                                                                                        <char>
#> 1:             excluded: EAD <= 0, missing default date or default after the observation date
#> 2:                          merged into the earlier default of the facility (window 9 months)
#> 3:                                          cash-flow rows dropped: no default event in scope
#> 4:                                open for 60 months or more: closed with no further recovery
#> 5: open workouts younger than t_max: expected further recovery added from the product profile
#> 6:                                                  floored at 0 in lgd_real (raw value kept)
#> 7:                                                      kept above 1 (lgd_cap_at_one = FALSE)
#>     kept
#>    <int>
#> 1:   885
#> 2:   885
#> 3:   885
#> 4:   885
#> 5:   885
#> 6:   885
#> 7:   885
head(wo$rds[, c("default_id", "product", "status", "lgd_raw", "lgd_real", "is_cure")])
#>    default_id   product status    lgd_raw   lgd_real is_cure
#>        <char>    <char> <char>      <num>      <num>  <lgcl>
#> 1:      D0660 unsecured  cured 0.03306260 0.03306260    TRUE
#> 2:      D0262 unsecured  cured 0.03609899 0.03609899    TRUE
#> 3:      D0506      auto  cured 0.05858313 0.05858313    TRUE
#> 4:      D0610  mortgage  cured 0.04705677 0.04705677    TRUE
#> 5:      D0516 unsecured closed 0.43716568 0.43716568   FALSE
#> 6:      D0560      auto closed 0.61276545 0.61276545   FALSE