sbtv {CreditRisk}

Scenario Barrier Time-Varying Volatility AT1P model

Description

sbtv calculates the survival probability Q(\tau > t) and default intensity for each maturity according to the structural SBTV model.

Usage

sbtv(V0, H, p, B, sigma, r, t)

Arguments

V0

firm value at time t = 0 (it is a constant value).

H

vector of differents safety level at time t = 0.

p

vector of the probability of different scenario (sum of p must be 1).

B

free positive parameter used for shaping the barrier Ht.

sigma

a vector of constant stepwise volatility \sigma_t.

r

a vector of constant stepwise risk-free rate.

t

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

Details

sbtv is an extension of the at1p model. In this model the parameter H0 used in the at1p model is replaced by a random variable assuming different values in different scenarios, each scenario with a different probability. The survival probability is calculated as a weighted avarage of the survival probability using the formula:

SBTV.Surv = \sum_{i = 1}^N p[i] * AT1P.Surv(H[i])

where AT1P.Surv(H[i]) is the survival probability computed according to the AT1P model when H_0 = H[i] and with weights equal to the probabilities of the different scenarios.

Value

sbtv returns an object of class data.frame containing the survival probability for each maturity. The last column is the default intensity calculated among each interval \Delta t.

References

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

Examples

mod <- sbtv(V0 = 1, H = c(0.4, 0.8), p = c(0.95, 0.05), B = 0, sigma = rep(0.20, 10),
            r = cdsdata$ED.Zero.Curve, t = cdsdata$Maturity)
mod

plot(cdsdata$Maturity, mod$Survival, type = 'b')