Merton {CreditRisk} | R Documentation |
Merton
calculates the survival probability Q(τ > T) for
each maturity according to the structural Merton's model.
Merton(L, V0, sigma, r, t)
L |
debt face value at maturity |
V0 |
firm value at time |
sigma |
volatility (constant for all t). |
r |
risk-free rate (constant for all t). |
t |
a vector of debt maturity structure. The last value of this vector rapresents the debt maturity T. |
In Merton's model the default event can occur only at debt maturity T and not before.
In this model the debt face value L
represents the constant safety
level. In this model the firm value is the sum of the firm equity value St
and
ad the firm debt value Dt
. The debt value at time t < T is calculated by the formula:
D_t = L * \exp^{- r * (T - t)} - Put(t, T; V_t, L)
The equity value can be derived as a difference between the firm value and the debt:
S_t = V_t - D_t = V_t - L * \exp^{- r * (T - t)} + Put(t, T; V_t, L) = Call(t, T; V_t, L)
(by the put-call parity) so that in the Merton's model the equity can be interpreted as a Call option on the value of the firm.
Merton
returns an object of class data.frame
with:
Vt
: expected Firm value at time t < T calculated by the simple formula
V_t = V_0 * \exp^{r * t}.
St
: firm equity value at each t < T. This value can be seen as a call
option on the firm value V_t
.
Dt
: firm debt value at each t < T.
Survival
: surviaval probability for each maturity.
Damiano Brigo, Massimo Morini, Andrea Pallavicini (2013) Counterparty Credit Risk, Collateral and Funding. With Pricing Cases for All Asset Classes
mod <- Merton(L = 10, V0 = 20, sigma = 0.2, r = 0.005, t = c(0.50, 1.00, 2.00, 3.25, 5.00, 10.00, 15.00, 20.00)) mod plot(c(0.50, 1.00, 2.00, 3.25, 5.00, 10.00, 15.00, 20.00), mod$Surv, main = 'Survival Probability for different Maturity \n (Merton model)', xlab = 'Maturity', ylab = 'Survival Probability', type = 'b')