The Explicit Corporate Yield Curve capital market simulator is built on top of the multi-factor term structure capital market simulator, so the first steps in the simulation are to calculate inflation, the real rate of interest and the entire term structure of government interest rates (that is, interest rates that are free of the risk of default and free of credit risk). See Multi-Factor Term Structure Simulation Type for a description of this process.

Once the risk-free interest rates have been determined, the Explicit Corporate Yield Curve simulator calculates the credit spread based on the thirteen bond spread parameters discussed under the Explicit Corporate Bond Spreads topic. The general process and assumptions are as follows:

• The long term (30 year) corporate spread is calculated first, based on the five long term spread parameters (mean, standard deviation and serial correlation of the spread plus its correlation with the long term government yield and with unexpected inflation). The credit spread is assumed to be lognormally distributed.

• Next the short term (1 year) corporate spread is calculated, based on the assumed correlation of the short and long term spreads and the five short term spread parameters (mean, standard deviation and serial correlation of the spread plus its correlation with the short term government yield and with unexpected inflation). As with the long term spread, the credit spread is assumed to be lognormally distributed.

• The corporate bond (spot) curve values are then calculated as the sum of the government zero coupon bond curve value at a duration and the simulated credit spread at that duration.

• The one year corporate bond return, labeled as the asset class NRcorp1 in the simulation output, is defined as the 1 year government return (NRgov1 in the simulation output) plus the short term corporate spread.

• The 30 year corporate bond return, labeled as the asset class NRcorp30 in the simulation output, is defined as the return on a 30 year bond (paying coupons semi-annually) purchased at par at year n-1 and then sold a year later (at year n). For this calculation, the credit spread used to determine the corporate bond spot rates at each of the 60 durations from 0.5 to 30 (half year intervals between durations) is determined by linearly interpolating between the short and long term spreads (using the short term spread for both durations 0.5 and 1).

• The corporate bond benchmark yield calculated by the simulator, and available for simulating retirement plan liabilities, is defined in each year as the current 30-year par coupon rate, the same coupon rate that will be used to determine the 30 year corporate bond return in the next simulation year.

Click the Yield Curve button (on the Capital Market Simulation dialog box) to display the values of the initial government and corporate spot curves (the yields on zero coupon bonds of duration t) and yield curves (the yields-to-maturity for coupon paying bonds of duration t) for integral durations from 1 to 30 years.

Once the spot and yield curves and the associated asset class returns (NRgov1, NRcorp1, NRgov30 and NRcorp30) have been simulated, returns on asset classes other than zero coupon bonds are determined based on the following regression equation:

NR(t) = a + [b * NRgov1] + [c * NRgov30] + [d * NRcorp1] + [f * NRcorp30] + e

For details about defining asset classes other than government and corporate bills and 30 year bonds, see Asset Classes and Asset Class Parameters.

See the discussion of calibrating simulators (multi-factor term structure type) for assistance in setting the parameters so that the simulated asset returns meet your expectations.

Once the simulator has been run, the Export button (on the Capital Market Simulation dialog box) is accessible.  This is a split button with two options:  Export Yield Curves and Export Simulation.  Click on the button directly to access the default option, Export Yield Curves, which  allows you to export simulated government and corporate bond spot yield curves to ProVal databases. In the next dialog box, to populate values in the Government yield curve database file, select an existing database or click New to create a new one. Similarly, to populate values in the Corporate Yield curve database file, select an existing database or click New. Note that if you wish to export both government and corporate yield curves, you must select different databases. The exported database(s) will have the structure and contents described under the Simulated Full Yield Curves topic of a custom capital market simulator and can be used as input for this topic of a custom simulator, either exactly as produced by the Explicit Corporate Yield Curve simulator or after editing (as described, again, under the Simulated Full Yield Curves topic).

Under the Database Properties command, the Change History tab for a database exported from an Explicit Corporate Yield Curve simulator will display “CMS Export” in the Tool column. The Description column will say whether the yield curves are government or corporate. The Notes tab will furnish information about the basis for the database export, including where these yield curves came from (such as the name and parameter settings of the Capital Market Simulation that produced this database).

Simulated full yield curve databases may be edited by use of the commands of the Edit Data command group on the Database Menu. The database contents may be displayed by selecting Spreadsheet Edit from this command group or by use of the Shortcuts pane (select “Databases”, then select the database from the list and double-click its name to open it). Alternatively, you may display database contents by using the List Data command of the Import / Export Data group of commands on the Database Menu. Summary yield curve statistics are available under the Frequency Tables and Descriptive Statistics commands of this menu.

The second option on the Export button, to Export Simulation, exports all of the capital market simulation results to a proprietary .cms file.  This feature is useful for clients using software products that are integrated with ProValPS and designed to import this type of file.