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LiborProcess
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Description
Class Summary  
Calibrator  This is a restricted version of a Libor process which has all the methods needed for calibration (computing the relevant prices at time zero, solving for implied volatilities etc) but no methods for path computation. 
CalibratorTest  A jUnit test suite for the class Calibrator . 
CS_FactorLoading  Implements the correlation and volatility structure from the document LiborProcess.ps which follows ideas of B. 
CS_FactorLoadingTest  Class of unit tests for the class CS_FactorLoading
in the jUnit testing framework. 
EP_FactorLoading  A factor loading with logLibor volatilities of the form
sigma_j(t)=c_jg(1t/T_j) with g(t)=1+Ah(t)
where h(t)=t(1t) and correlations rho_ij=b_i/b_j ,
for i<=j, with b_i=exp(beta*i^alpha) . 
FactorLoading  This class provides access to the factor loadings nu_i(s)
in the form of the Libor volatilities sigma_i(t) and
correlations rho_ij . 
JR_FactorLoading  Implements the correlation and volatility structure from Jaeckel's book Monte Carlo Methods in Finance. 
JR_FactorLoadingTest  Class of unit tests for the class CS_FactorLoading
in the jUnit testing framework. 
LiborProcess  The basic class simulating Libor paths as well as the paths of two
lognormal approximations (X0,X1 , see LiborProcess.ps). 
LiborProcessTest  Class of unit tests for the class LiborProcess
in the jUnit testing framework. 
LiborVector  The RandomVector of Libors
U=(X_m(T_m),X_{m+1}(T_m),...,X_{n1}(T_m)) as seen from time
t=0 , ie. 
LMM_Parameters  Class which combines an initial term structure l[j]=L_j(0)
with a FactorLoading object and hence provides everything
to set up a Libor process. 
SyntheticData  This class has static methods to produce a set of caplet and swaption
prices from the analytic pricing formulas in two separate files
CapletFile and SwaptionFile in the precise format
in which a Calibrator object expects these files for reading in the
data. 
LiborProcess
Implementation of the Libor Market Model (LMM) with deterministic forward Libor volatilities and constant correlations. Path simulation relies on a predictor corrector algorithm and paths step directly from one point on the tenor structure to the next. Consequently this implementation is not useful in situations where forward Libors must be evaluated at times between Libor reset dates.
A detailed description of the theory behind the implementation and the
notation and terminology is contained in the document LiborProcess.ps.
All the information regarding the volatility and correlation structure is
contained in the abstract class FactorLoading.
With forward Libor
L_i
satisfying the dynamics
dL_i(t)=L_i(t)[BC_i(t)dt+BD_i(t)dW(t)]
the factor loading
of L_i
is the W
integrable process BD_i
. These
factor loadings are accessed through the volatilities sigma_i(t)
and correlations rho_ij
. See LiborProcess.ps for details.
Two examples of factor loadings are implemented. One is a class based on
ideas of B. Coffey and J. Schoenmakers the other is a test class with the sole
purpose of producing synthetic data which can be used for calibration
experiments with the CoffeySchoenmakers structure.
There is a range of ideas regarding the proper construction of a correlation
and volatility structure. The modularity of this program allows you to define
your own volatilities and correlations and to plug them into the framework
quite easily. All that is necessary is to derive from the class
FactorLoading
and to define the abstract methods which are the
instantaneous loglibor correlations rho_ij
, the volatility
functions sigma_i(t)
and covariation integrals
<log(L_i),log(L_j)>_t^T=integral_t^T cv_ij(s)ds,
where
cv_ij(s)=sigma_i(s)sigma_j(s)rho_ij=nu_i(s).nu_j(s).
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