calibrate.BlackCox: Black and Cox model calibration to market CDS data
Description
Compares CDS rates quoted on the market with theoric CDS rates calculeted by the function
cds and looks for the parameters to be used into BlackCox
for returning the default intensities corresponding to real market CDS rates performing the
minimization of the objective function.
Usage
calibrate.BlackCox(V0, cdsrate, r, t, ...)
Arguments
V0
firm value at time t = 0.
cdsrate
CDS rates from the market.
r
risk-free rate.
t
a vector of debt maturity structure.
...
additional parameters used in cds function.
Value
calibrate.BlackCox returns an object of class data.frame with calculated parameters of
the BlackCox model and the error occurred in the minimization procedure.
Details
Inside calibrate.BlackCox, the function objfn takes the input a
vector of parameters and returns the mean error occurred estimating CDS rates with
cds function. The inputs used in cds are the default intensities calculated by
the BlackCox function with the calibrated parameters. In particular the error is
calculated as:
$$\frac{1}{n}\sum_{i=1}^n (c^{ds}-c^{ds}_{mkt})^2.$$ This quantity is a function of
the default intensities and it is the objective function to be minimized in order to take
optimal solutions for intensities.
References
Damiano Brigo, Massimo Morini, Andrea Pallavicini (2013)
Counterparty Credit Risk, Collateral and Funding.
With Pricing Cases for All Asset Classes