Simulating Interest Rates
Overview
Simulating interest rates can be a difficult task. The primary issue is that you will
generally need to simulate the whole interest rate curve, instead of just a single point.
Most models that use semi-realistic assumptions about
the evolution of the curve often create simulated curves that are unrealistic, typically because they violate certain smoothness assumptions
On other hand, sometimes you may need to simulate interest rates at all, or you may be able to make some simplifications that allow you
to reduce the problem.
Note - this discussion is about simulating interest rates under the real measure, not the
risk neutral measure
that is commonly used in pricing interest rate derivatives.
Situations that Require Simulating Interest Rates
- Pre-payments - when you decide to simulate pre-payments, you will generally need to simulate the interest rates.
Alternatively
-
Reinvestments - when you simulate a portfolio over a given time frame, a decision must be made about what to do with cash flows
that are generated by the portfolio. If the portfolio represents a
structure security,
you may generally assume that the cash flows are directed to the holders of the security, although there may be situations where
some of the cash is retained. Otherwise, if the portfolio represents the holdings of some going-concern, the cash flows will need
to be re-invested and those re-investments simulated.
Methods of Simulating the Interest Rate
