cds {CreditRisk}

Calculates Credit Default Swap rates

Description

Calculates CDS rates starting form default intensities.

Usage

cds(t, int, r, R = 0.005, RR = 0.4, simplified = FALSE)

Arguments

t

premium timetable.

int

deterministic default intensities vector.

r

spot interest rates.

R

constant premium payments, value that the buyer pays in each t_i.

RR

recovery rate on the underline bond, default value is 40%.

simplified

logic argument. If FALSE calculates the CDS rates using the semplified version of calculations, if TRUE use the complete version.

Details

• Premium timetable is t_i; i=1,...,T. The vector starts from t_1\le 1, i.e. the first premium is payed at a year fraction in the possibility that the bond is not yet defaulted. Since premium are a postponed payment (unlike usual insurance contracts).

• Intensities timetable have domains \gamma_i; i=t_1,...,T.

• spot interest rates of bond have domain r_i; i=t_1,...,T. The function transforms spot rates in forward rates. If we specify that we want to calculate CDS rates with the simplified alghoritm, in each period, the amount of the constant premium payment is expressed by:

  \pi^{pb}=\sum_{i=1}^Tp(0,i)S(0,i)\alpha_i

  and the amount of protection, assuming a recovery rate \delta, is:

  \pi^{ps}=(1-\delta)\sum_{i=1}^Tp(0,i)\hat{Q}(\tau=i)\alpha_i

  If we want to calculate same quantities with the complete version, that evaluate premium in the continous, the value of the premium leg is calculated as:

  \pi^{pb}(0,1)=-\int_{T_a}^{T_b}P(0,t)\cdot(t-T_{\beta(t)-1}) d_t Q (\tau\geq t)+\sum_{i=a+1}^bP(0,T_i)\cdot\alpha_i * Q(\tau\geq T_i)

  and the protection leg as:

  \pi_{a,b}^{ps}(1):=-\int_{t=T_a}^{T_b}P(0,t)d*Q(\tau\geq t)

  In both versions the forward rates and intensities are supposed as costant stepwise functions with discontinuity in t_i

Value

cds returns an object of class data.frame with columns, for esch date t_i the value of survival probability, the premium and protection leg, CDS rate and CDS price.

References

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

Examples

cds(t = seq(0.5, 10, by = 0.5), int = seq(.01, 0.05, len = 20),
r = seq(0,0.02, len=20), R = 0.005, RR = 0.4, simplified = FALSE)