Create LIBOR Market Model
The LIBOR Market Model (LMM) differs from short rate models in that it evolves a set of discrete forward rates. Specifically, the lognormal LMM specifies the following diffusion equation for each forward rate
$$\frac{d{F}_{i}(t)}{{F}_{i}}={\mu}_{i}dt+{\sigma}_{i}(t)d{W}_{i}$$
where:
W is an Ndimensional geometric Brownian motion with
$$d{W}_{i}(t)d{W}_{j}(t)={\rho}_{ij}$$
The LMM relates the drifts of the forward rates based on noarbitrage arguments. Specifically, under the Spot LIBOR measure, the drifts are expressed as
$${\mu}_{i}(t)={\sigma}_{i}(t){\displaystyle \sum _{j=q(t)}^{i}\frac{{\tau}_{j}{\rho}_{i,j}{\sigma}_{j}(t){F}_{j}(t)}{1+{\tau}_{j}{F}_{j}(t)}}$$
where:
$${\tau}_{i}$$ is the time fraction associated with the i th forward rate
q(t) is an index defined by the relation
$${T}_{q(t)1}<t<{T}_{q(t)}$$
and the Spot LIBOR numeraire is defined as
$$B(t)=P(t,{T}_{q(t)}){\displaystyle \prod _{n=0}^{q(t)1}(1+{\tau}_{n}{F}_{n}({T}_{n}))}$$
OBJ = LiborMarketModel(ZeroCurve,VolFunc,Correlation)
constructs
a LIBOR Market Model object.
For example:
Settle = datenum('15Dec2007'); CurveTimes = [1:5 7 10 20]'; ZeroRates = [.01 .018 .024 .029 .033 .034 .035 .034]'; CurveDates = daysadd(Settle,360*CurveTimes,1); irdc = IRDataCurve('Zero',Settle,CurveDates,ZeroRates); LMMVolFunc = @(a,t) (a(1)*t + a(2)).*exp(a(3)*t) + a(4); LMMVolParams = [.3 .02 .7 .14]; numRates = 20; VolFunc(1:numRates1) = {@(t) LMMVolFunc(LMMVolParams,t)}; Beta = .08; CorrFunc = @(i,j,Beta) exp(Beta*abs(ij)); Correlation = CorrFunc(meshgrid(1:numRates1)',meshgrid(1:numRates1),Beta); LMM = LiborMarketModel(irdc,VolFunc,Correlation,'Period',1);
The following properties are from the LiborMarketModel
class.

Attributes:
 

Attributes:
 

Attributes:
 

Number of Brownian factors. The default is Attributes:
 

Period of the forward rates. The default is
Attributes:

simTermStructs  Simulate term structures for LIBOR Market Model 
The LIBOR Market Model, also called the BGM Model (Brace, Gatarek, Musiela Model) is a financial model of interest rates. The quantities that are modeled are a set of forward rates (also called forward LIBORs) which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts.
Brigo, D. and F. Mercurio. Interest Rate Models  Theory and Practice. Springer Finance, 2006.