QL_Market_Model

The disclaimer described in QL MM Data applies also here.

It describes an interest rate model, where the starting point is the assumption that each forward interest rate in a certain set of rates follows a specific diffusion with respect to a respective measure.

The important features here are:

a) Initially only a certain discrete set of forward rates is modelled, rather than the short rate or any single forward rate.

b) The chosen forward rates are modelled simultaneously but each with respect to a different probability measure.

The forward rates may be either ibor rates or swap rates, resulting respectively to a "libor market model" or "swap market model".

It is not possible to have both libor and swap rates in the same model because it is proven that the resulting diffusions are not mutually compatible.

The reason for modelling each forward rate with respect to a separate measure is in order to make all rates appearing as being martingales, which would not be possible if all rates were modelled wrt a common measure.

Being martingales, the chosen forward rates can be further assumed to follow a lognormal process, just like the forward stock price in the Black Scholes world.

In order to accomodate negative interest rates, a slight modelling extension is often adopted, whereby it is assumed that the sum

Each forward rate may have its own separate diplacement amount