Stressed PD of the one-factor model

The conditional PD at confidence q: N((G(pd) + sqrt(rho) G(q)) / sqrt(1 - rho)). With q = 0.999 and the regulatory correlation it is the PD inside the risk-weight function, so that the capital requirement of a retail exposure is lgd * (scr_pd_stress(pd, r, 0.999) - pd). Used by the sensitivity grid of scr_capital() and by the scenario engine of scr_ecl(). Arguments are recycled.

Usage

scr_pd_stress(pd, rho, q)

Arguments

pd

Numeric vector of unconditional PDs.

rho

Asset correlation in [0, 1).

q

Confidence level in (0, 1); 0.5 returns the median-year PD.

Value

A numeric vector of conditional PDs.

References

Vasicek, O. (2002). The distribution of loan portfolio value. Risk, 15(12), 160-162. Gordy, M. B. (2003). A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation, 12(3), 199-232.

See also

scr_pd_pit_ttc(), the same bridge with the systematic factor given as a value of z rather than a quantile q.

Other irb-capital: scr_capital(), scr_ecl(), scr_el(), scr_irb_rw(), scr_sa_rw()

Examples

scr_pd_stress(0.02, rho = 0.15, q = c(0.5, 0.95, 0.99, 0.999))
#> [1] 0.01295348 0.06219237 0.10558734 0.17632894