Interest Rate Curve Calibration with
Problem raised by Indizen
Technologies S.L.
Coordinating teachers of the problem:
Gerardo Oleaga (Universidad
Complutense de Madrid)
Jorge
Valdehita Prieto (Indizen Technologies S.L.)
Exposition of the problem:
The value of an interest rate curve at a future time can be known today
and can help us to obtain today's values for fixed income securities, futures,
derivatives, etc. However, if we move forward in time and wish to know the
value of those securities in the future, then the interest rate curves ought to
be simulated.
A
Every point on the given interest rate curve is a different Risk Factor
to be simulated. To simplify the problem, let's consider for each Risk Factor a
Log-Normal Geometric Brownian Motion as follows:
Given historical series for each Risk Factor from the interest rate
curve, some statistical measures such as 
and 
ought to
be calculated in order to simulate different scenarios.
Curve Calibration for the interest rate curves is the next step to be
considered in order to obtain curves that show what truly happens in the
market. For instance, a simple simulation will consider short and long term
interest rate structures as equal.
The Nelson-Siegel Model is a
parametric estimation technique for yield curves. It is a non-polynomial model
to prevent abrupt changes in the term structure of interest rates, mostly for
the long term.
, where 
, 
and 
indicate the
contribution of long, short and medium term components respectively; 
is the decay
factor and m is the time to maturity.
Scheme of the work to be done:
1) Do a simple
MonteCarloSimulator in Matlab to produce interest rate curve scenarios with a
Log-Normal evolution model for each TimeStep.
2) Write a
Matlab function named NelsonSiegelCalibration to perform the calibration method
for the interest rate curves. Calibrate the corresponding Risk Factors from the
curve with the given historical series. A historical series for the parameters is then produced. Now, use the
MonteCarloSimulator to produce different interest rate calibrated curves for
each TimeStep assuming that the parameters have a Log-Normal evolution model.
Compare the results to the ones obtained from the usual simulation.
3) Conclusions
and Consequences. Does the calibration produce interest rate curves similar to
the ones in the market? Is it reasonable that the parameters have the same
evolution model as the curve? If not, can you tell how the parameters are
distributed? Can you think of other ways to produce a calibration for interest
rate simulated curves?