Forecast Yield Curves
The Forecast Yield Curves command allows you to input and store, for future valuation dates in a forecast, duration-based valuation interest rate assumptions. These yield curve library entries may be used later to forecast interest rates in a Deterministic Forecast, by selecting the Forecast Yield Curve Library entry under the Future Valuation Interest Rates topic of the Deterministic Assumptions command. They are also used to override first and/or second year yield curves in a Stochastic Forecast, by selecting the Forecast Yield Curve Library entry under the First & Second Year Simulation Overrides topic of the Stochastic Assumptions command.
You may specify interest rates separately for each forecast valuation date, with the first forecast valuation date (one year after the baseline Valuation Date) denoted as Fcst Yr 1, the second forecast valuation date (two years after the baseline Valuation Date) denoted as Fcst Yr 2, and so forth. For each forecast valuation date, the duration of each rate is measured from that forecast valuation date (not from the baseline valuation date).
The last column of rates entered will be used for all subsequent forecast years. The last row of rates entered will be used for all subsequent durations.
Enter rates in the spreadsheet as decimal equivalents, not percentages (e.g., for 6%, enter 0.06).
Name is a text field for entering a description of the Forecast Yield Curve being defined.
Select Define curves using rates at bendpoints to specify, for each Fcst Year (forecast valuation date), interest Rates at up to three Bendpoints, using the three bend point parameters for the rates to be used starting at durations 0, m and n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint. Note that ProVal presumes the three rates entered are 24 month averages of segment rates.
The Type parameter tells ProVal how to interpret the rates entered:
If you select segment rates, ProVal will create the yield curve by keeping the specified interest rate constant from the duration corresponding to the bend point for which it is entered until the duration corresponding to the next specified bend point (if any); that is, the interest rate is constant between the bend points. The segment rate at the duration specified for the last bend point entered will be used for all longer durations. Thus each specified interest rate represents a portion of the yield curve that is flat until the next specified rate (if any), or level between bendpoints. The three columns of the Rates grid are labeled Segment rate from duration 0 up to m, Segment rate from duration m up to n and Segment rate from duration n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint.
If you select full yield curve, ProVal will interpolate between the interest rate points provided and extrapolate beyond the last point entered (if necessary) to create the full yield curve, by fitting a reasonable curve to the points provided. Thus the specified interest rates, once interpolated, form a graduated full yield curve that is changing between bendpoints (rather than flat). For extrapolation purposes, the yield curve is assumed to flatten out at durations greater than the last bend point entered but not before duration 30 (that is, if the last specified bend point is at a duration shorter than 30, the yield curve will not flatten out until duration 30). The three columns of the Rates grid are labeled Rate at duration 0, Rate at duration m and Rate at duration n, where m is the value entered for the second Bendpoint and n is the value entered for the third Bendpoint.
Select Input rates at every duration, and click the Rates... button, to specify interest rates for every forecast valuation date (columns) at every duration (rows). Note that rates for the last forecast year (column) specified will be used for all subsequent forecast years. Similarly, rates for the last duration specified will be used for all subsequent durations. The From column may be changed if you wish to define an interest rate for consecutive durations. The Up to column indicates the ending duration for each specified interest rate; its values depend on your entries in the From column and cannot be changed.
Forward versus spot rates
In a deterministic forecast, regardless of whether you are defining curves by using rates at bend points or inputting rates at every duration, the nature of the valuation assumption interest rate determines how the forecast yield curve is interpreted:
| Valuation assumption | Forecast yield curve interpreted as... |
| segment rates | spot rates |
| spot rates | spot rates |
| forward rates | forward rates |
| variable by calendar year | forward rates |
| constant rate | user-directed |
In a stochastic forecast, the forecast yield curve is always interpreted as spot rates (to override the spot rates simulated in the capital market simulation) regardless of the valuation assumption.
The If the valuation assumption is a constant interest rate, the rates above are parameter is only applicable in a deterministic forecast and when the valuation assumption is a constant interest rate. If the valuation assumption is a constant interest rate, specify whether the yield curve rates entered above are spot rates or forward rates. For details on spot versus forward rates, see Interest Rates.