The Applied Financial Technology Interest Rate Process is a trading quality (arbitrage free) interest rate process that is uniquely able to simultaneously price ITM and OTM caps, floors and swaptions. This unique ability is highly desirable when performing calculations for MBS.

Interest rate generation process

There have been numerous attempts to generate a set of possible future interest rate realizations that is completely arbitrage free and consistent with the term structure of interest rates and volatilities.

There is another requirement as well - the process should have a tree implementation for a straight-forward evaluation of American style options. In addition, probably the most important requirement is that it should take a finite computation time.

All the existing processes have fallen short of these requirements until recently. CIR and BDT type processes cannot fit existing complex volatilities term structures. HJM tree implementation becomes computationally untenable beyond 8-9 time nodes. The HJM simulation implementation requires many thousands of paths to start converging, needing a super computer to calculate even a simple CMO OAS, and it does not allow for a tree implementation.

AFT has developed a model that satisfies all of the above requirements. This state-of-the-art interest rate process creates a two-dimensional tree structure (three dimensional if time dimension is included) that can fit an arbitrary volatilities term structure as well as an interest rate term structure.

It takes about 10 seconds to fit the tree to the yield curve on a Pentium 200 computer.

The interest rate process is a log-normal, mean reverting, two-factor process. Mean reversion is a function of time and can be set by the user to be anything, including zero. The first factor defines the volatility of interest rates; the second defines volatility of the slope of the yield curve. The volatilities are time-varying with a user supplied correlation.

Mathematical details

It can be shown that v is the excess slope of the yield curve for a given time on a given node vs. the  average expected slope.

It can also be shown that the correlation between changes in the slope and changes in the short rate is

Interest rate process fitting routines

AFT's fitting routines solve for volatility parameters so that prices generated from the tree equal current market prices for the entire term structure of caps and swaptions.