Nelson Siegel Risk Model
The Nelson Siegel Model can be used to calculate a fixed income market risk. That is, if the daily differences of the parameters of the model are assumed to have statistical distribution, then the expected (and unexpected) gains and losses of a specified portfolio can be calculatedParameter Difference Simulations
The following chart shows the differences of the level parameter. They are charted in a histogram.The chart resembles a normal distribution as one might assume by recalling the law of large numbers. One can use the moments library to calculate the mean and standard deviation of the differences, and the utilize the normal api to simluate random draws.
Discounting the Portfolio
In order to calculate changes in the market value of a fixed income portfolio, you will need to calculate the cash flows from the underlying instruments. (see forecasting cash flows)Next, for each cash flow, a present value is calculated at current interest rates. This gives the market value of the portfolio now.
A simulation is performed as above, where a set of new Nelson Siegel parameters are calculated, and a new present value is calculated.
Dependency Structures
- Correlated Parameter Differences - it is probably unrealistic to