sbtv {CreditRisk} R Documentation

## Scenario Barrier Time-Varying Volatility AT1P model

### Description

`sbtv` calculates the survival probability Q(τ > 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 σ_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 = ∑_{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 Δ 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')

```

[Package CreditRisk version 0.1.3 Index]