Merton {CreditRisk} | R Documentation |
Merton's model
Description
Merton
calculates the survival probability Q(\tau > T)
for
each maturity according to the structural Merton's model.
Usage
Merton(L, V0, sigma, r, t)
Arguments
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. |
Details
In Merton 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 model the equity can be interpreted as a Call option on the value of the firm.
Value
Merton
returns an object of class data.frame
with:
-
Vt
: expected Firm value at timet < T
calculated by the simple formulaV_t = V_0 * \exp(r t)
. -
St
: firm equity value at eacht < T
. This value can be seen as a call option on the firm valueV_t
. -
Dt
: firm debt value at eacht < T
. -
Survival
: survival probability for each maturity.
References
Damiano Brigo, Massimo Morini, Andrea Pallavicini (2013) Counterparty Credit Risk, Collateral and Funding. With Pricing Cases for All Asset Classes
Examples
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')