# PTMultiPeriodPD: Multi-period Pluto and Tasche Model In LDPD: Probability of Default Calibration

## Description

Estimates probability of default (PD) according to Multi-period Pluto & Tasche model.

## Usage

 `1` ```PTMultiPeriodPD(portf.uncond, portf.def, rho, cor.St, kT, kNS = 1000, conf.interval = 0.9) ```

## Arguments

 `portf.uncond` Unconditional portfolio distribution (e.g. number of counterparts by rating classes). `portf.def` Number of defaults by rating classes. `rho` Correlation with systematic factor. `cor.St` Correlation matrix of systematic factor realization through the time. In case constant is given - power matrix is used: Correlation matrix (i, j) = cor.St ^ |s - t|, s = 1..kT, t = 1..kT. `kT` Number of periods used in the PD estimation. `kNS` Number of simulations for integral estimation (using Monte-Carlo approach). `conf.interval` Confidence interval for PD estimation.

## Details

Estimates probabilities of default according to multi-period Pluto and Tasche model (additionally captures the inter-temporal correlation effects).

## Value

Conditional PDs according to Multi-period Pluto and Tasche model

## Note

Portfolio and default data should be sorted by rating classes from lowest credit quality to higher one.

## Author(s)

Denis Surzhko <densur@gmail.com>

## References

Pluto, K. and Tasche, D., 2005. Thinking Positively. Risk, August, 72-78.

`PTOnePeriodPD`

## Examples

 ```1 2 3``` ```portfolio <- c(10,20,30,40,10) defaults <- c(1,2,0,0,0) PTMultiPeriodPD(portfolio, defaults, 0.3, cor.St = 0.3, kT = 5, kNS = 1000, conf.interval = 0.5) ```

### Example output

```[1] 0.04284042 0.03299894 0.01780414 0.01146315 0.01053244
```

LDPD documentation built on May 1, 2019, 7:56 p.m.