BlackCox {CreditRisk} | R Documentation |

`BlackCox`

calculates the survival probability *Q(τ > t)* and default intensity
for each maturity according to the structural Black and Cox's model.

BlackCox(L, K = L, V0, sigma, r, gamma, t)

`L` |
debt face value at maturity |

`K` |
positive parameter needed to calculate the safety level. |

`V0` |
firm value at time |

`sigma` |
volatility (constant for all t). |

`r` |
risk-free rate (constant for all t). |

`gamma` |
interest rate used to discount the safety level |

`t` |
a vector of debt maturity structure (it is a numeric vector). |

In Merton's model the default event can occurr only at debt maturity *T* while
in Black and Cox's model the default event can occurr even before.
In this model the safety level is given by the output `Ht`

. Hitting this barrier is
considered as an erlier default. Assuming a debt face value of `L`

at the final
maturity that coincides with the safety level in *t = T*, the safety level in *t≤ T* is the
`K`

, with *K≤ L*, value discounted at back at time *t* using the interest rate
`gamma`

, obtaining:

*H(t | t≤ T) = K * \exp^{- γ * (T- t)}*

The output parameter `Default.Intensity`

represents the default intensity of
*Δ t*. The firm's value `Vt`

is calculated as in the `Merton`

function.

This function returns an object of class `data.frame`

containing firm value, safety level *H(t)*
and the survival probability for each maturity. The last column is the default intensity calculated
among each interval *Δ t*.

David Lando (2004) Credit risk modeling.

Damiano Brigo, Massimo Morini, Andrea Pallavicini (2013) Counterparty Credit Risk, Collateral and Funding. With Pricing Cases for All Asset Classes.

mod <- BlackCox(L = 0.55, K = 0.40, V0 = 1, sigma = 0.3, r = 0.05, gamma = 0.04, t = c(0.50, 1.00, 2.00, 5.00, 7.00, 10.00, 20.00, 30.00)) mod plot(c(0.50, 1.00, 2.00, 5.00, 7.00, 10.00, 20.00, 30.00), mod$Ht, type = 'b', xlab = 'Maturity', ylab = 'Safety Level H(t)', main = 'Safety level for different maturities', ylim = c(min(mod$Ht), 1.5), col = 'red') abline(h = 0.55, col = 'red') lines(c(0.50, 1.00, 2.00, 5.00, 7.00, 10.00, 20.00, 30.00), mod$Vt, xlab = 'Maturity', ylab = 'V(t)', main = 'Value of the Firm \n at time t', type = 's') plot(c(0.50, 1.00, 2.00, 5.00, 7.00, 10.00, 20.00, 30.00), mod$Survival, type = 'b', main = 'Survival Probability for different Maturity \n (Black & Cox model)', xlab = 'Maturity', ylab = 'Survival Probability') matplot(c(0.50, 1.00, 2.00, 5.00, 7.00, 10.00, 20.00, 30.00), mod$Default.Intensity, type = 'l', xlab = 'Maturity', ylab = 'Default Intensity')

[Package *CreditRisk* version 0.1.3 Index]