Interest Rate Forecast Methods

19.4 Interest Rate Forecast Methods

The following Interest Rate Forecast methods are available.

Table 19-3 Interest Rate Forecast Methods

Method	Description
Flat	Forecast no change in the interest rate for all dates beginning with the as-of date.
Structured Change	Forecast rate changes in terms of absolute or percent change, for any modeling period or interest rate term, such as: +100 basis points on Day 1 -200 basis points over the first 6 months Yield curve rotation (short point decreasing, long point increasing)
Direct Input	Type interest rates directly for any modeling period or interest rate term.
Implied Forward	Forecast interest rates based on the yield-curve interest rates in effect at the as-of date and consistent with the modeling bucket definitions.
Change from Base	Make incremental changes to an existing forecast scenario.
Yield Curve Twist	Flatten or steepen the yield curve around a specific point on the curve.
Standardized Approach Shocks	Forecast an interest rate shock according to one of the BSCB Standardized Approach shock specifications (Scenario-level specification).
Enhanced Approach Shocks	Forecast an interest rate shock according to user specifications that will flow into IRRBB Table B reporting.

The following Interpolation Methods are available.

Table 19-4 Interpolation Methods

Method	Description
Linear Interpolation	Linear interpolation uses linear yield curve smoothing. Linear yield curves are continuous but not smooth; at each knot point there is a kink in the yield curve. You may not want to use a linear yield curve with a model that assumes the existence of a continuous forward rate curve, due to the nonlinear and discontinuous knot points of a linear yield curve.
Cubic Spline of Yields	A cubic spline is a series of third-degree polynomials that have the form: y = a + bx + cx² + dx³ These polynomials are used to connect the dots formed by observable data. The polynomials are constrained so they fit together smoothly at each knot point (the observable data point.) This means that the slope and the rate of change in the slope with respect to time to maturity have to be equal for each polynomial at the knot point where they join. If this is not true, there is a kink in the yield curve and they are continuous but not differentiable. Two more constraints make the cubic spline curve unique. The first restricts the zero-maturity yield to equal the 1-day interest rate. The second restricts the yield curve at the longest maturity to be either straight (y"=0) or flat (y'=0).
Quartic Spline	Quartic interpolation requires a minimum of 4 knot points. The quartic interpolation equation can be represented as: Y = a + b X¹ + CX² + d X³ + e X⁴ The end knot points satisfy equations for one curve and all intermediate points satisfy two curves. Hence in a scenario with a minimum number of knot points, there will be 6 equations. For n number of knot points, the number of equations is 2n-2. If n is the number of points to be interpolated, the order of the matrix to be formed is 5(n-1) x 5(n-1). The matrix is formed according to the following logic: The second derivative at the endpoints and the first derivative of the last point is Zero. At the points other than the endpoints, the value of the first derivatives, second derivatives, and the third derivatives of the function are equal.

Method

Description

Linear Interpolation

Linear interpolation uses linear yield curve smoothing. Linear yield curves are continuous but not smooth; at each knot point there is a kink in the yield curve. You may not want to use a linear yield curve with a model that assumes the existence of a continuous forward rate curve, due to the nonlinear and discontinuous knot points of a linear yield curve.

Cubic Spline of Yields

A cubic spline is a series of third-degree polynomials that have the form:

y = a + bx + cx² + dx³

These polynomials are used to connect the dots formed by observable data. The polynomials are constrained so they fit together smoothly at each knot point (the observable data point.) This means that the slope and the rate of change in the slope with respect to time to maturity have to be equal for each polynomial at the knot point where they join. If this is not true, there is a kink in the yield curve and they are continuous but not differentiable.

Two more constraints make the cubic spline curve unique. The first restricts the zero-maturity yield to equal the 1-day interest rate. The second restricts the yield curve at the longest maturity to be either straight (y"=0) or flat (y'=0).

Quartic Spline

Quartic interpolation requires a minimum of 4 knot points. The quartic interpolation equation can be represented as:

Y = a + b X¹ + CX² + d X³ + e X⁴

The end knot points satisfy equations for one curve and all intermediate points satisfy two curves. Hence in a scenario with a minimum number of knot points, there will be 6 equations. For n number of knot points, the number of equations is 2n-2. If n is the number of points to be interpolated, the order of the matrix to be formed is 5*(n-1) x 5*(n-1). The matrix is formed according to the following logic:

The second derivative at the endpoints and the first derivative of the last point is Zero. At the points other than the endpoints, the value of the first derivatives, second derivatives, and the third derivatives of the function are equal.

In looking up the Forecast Rates, the Cash Flow Engine will (where necessary) perform an interpolation between yield curve term points. For example, in determining a three-month rate from a yield curve that contains only a one-month rate and a six-month rate, the Cash Flow Engine will perform an interpolation to determine the implied three-month rate. The Interpolation method used is defined by the selected interpolation method for the Interest Rate Curve.

Note

You must supply the input data for all term points of an IRC. This applies to historical rate and direct input forecast method. If data of one or more terms points is not given, then it can lead to errors during calculation.

Examples of Interest Rate Forecasting

You can generate the forecast rates for 360 calendar months, Moody's structured cashflow library's integration is done with ALM. The first month corresponds to the first calendar month of As of Date. The subsequent months are full calendar months. For example, if As of Date is 30 APR 2013, then the first month is April 2013. The second month will be May 2013 and so on. ADCo model requires two IRCs for an ARM instrument (First is 2 Yr, 10 Yr IRC and second is the Prepayment Index IRC). For a fixed-rate instrument, 2 Yr, 10 Yr IRC will only be passed.

You can forecast an IRC which has various term points including 2 Year and 10 Year term points. The term points 2 Year (or 24 Months) and 10 Year (or 120 Months) are available. The engine will identify 24 Months term point as 2 Years and 120 Months as 10 Years. If the term point (or points) are unavailable, then the engine will be unable to send the forecast rates for the IRC.

The engine will match the last day of the calendar month with the income simulation bucket (ISB) dates and fetch the rate corresponding to the term point to pass to the ADCo model while converting from ISB to 360 months. While converting from ISB to 360 months, if the total ISB size is less than 360 months, then the last available rate must be extended till the 360th month. For example, if the ISB covers only 240 months, then the 240th month rate will be applied from the 241st to 360th months.

When Show 360 months Buckets check box is enabled, 2-year (24 months) and 10-year (240 months) term points will be highlighted in red color.

The Show 360 months Buckets check box is displayed only if the Curve Identifier is defined for base IRC.

Flat: Viewing U. S. dollar interest rates forecasted for the Treasury Index.

From Currency Codes, select USD: US Dollar.
From Interest Rate Codes, select US Treasury Curve.
From Rate Forecast Method, select Flat.
Select the Interpolation method.
Click View.

After clicking View, the Interest Rate View window displays the rates forecasted for the Treasury Index in the ISB view. Here, Show Rates for Show 360 Months Buckets check box is not selected by default. On seecting this check box, the results will be displayed for the 360 months view. You can not enter the values against buckets for Flat method in 360 months or ISB view. The Show 360 Months Buckets check box is available by default if the ADCo LDM, Moody's structured cashflow library, or both functions are mapped to you.

Structured Change: Model a gradual increase for six months in U. S. dollar interest rates.

From Currency Codes, select USD: US Dollar.
From Interest Rate Codes, select US Treasury Curve.
From Rate Forecast Method, select Structured Change.
Select the Interpolation method.
Click Define and enter a shock amount to apply to the IRC in absolute or percentage change. You can designate either absolute rate change or percent rate change.
Enter the Interest Rate changes.
Use the Excel Import or Export feature to add the interest rate changes. For more information, see the Excel Import or Export section.
Click Apply.
Click View in Forecast Rates window.
After clicking View, the Interest Rate View window displays the rates forecasted for the Treasury Index in the ISB view. Here, Show Rates for Show 360 Months Buckets check box is not selected by default. On selecting this check box, the results will be displayed for the 360 months view. You cannot enter the values against buckets for Flat method in 360 months or ISB view. The Show 360 Months Buckets check box is available by default if the ADCo LDM, Moody's structured cashflow library, or both functions are mapped to you.

The rate increases you entered in step 5 are apportioned equally over six months in this case August to January. Therefore, in monthly buckets 2-7, you will expect to see the following increments added to the Treasury Index Interest Rates.

Table 19-5 Example of Structured Change

3 month	6 month	1 year	2 year
1/6 of 1.00 = 0.1667	1/6 of 1.25 = 0.2083	1/6 of 1.50 = 0.25	1/6 of 1.75 = 0.2917

3 month

6 month

1 year

2 year

1/6 of 1.00 = 0.1667

1/6 of 1.25 = 0.2083

1/6 of 1.50 = 0.25

1/6 of 1.75 = 0.2917

The interest rates in buckets 2-7 reflects the increases.

Direct Input: To use the Direct Input method, see the Structured Change sections with the following modifications:

In step 5, enter Interest Rates (forecasted rates for each bucket rather than forecasted rate changes over a period of one or more buckets).
In step 3, select Direct Input.
During defining the Direct Input, Show 360 Months Buckets check box is selected by default if the ADCo LDM, or Moody's structured cashflow library, or both functions are mapped to you. If you enter the forecast rates against 360 months, the UI converts the same across the Income Simulation Buckets.
Similarly, you can enter the data for income simulation buckets after unchecking the Show 360 Months Buckets. Now, the UI converts the rates from ISB to 360 months view.
When you switch from the ISB to 360 months view or vice versa, you will get a message: Switching the view will erase the existing definition. Do you want to continue? . Click YES to erase the definition.
- Enter the data across ISB and select the Show 360 Months Buckets check box, it overrides that data for a few of the 360 months buckets.
- Enter the data across 360 months buckets and do not select the Show 360 Months Buckets check box, it overrides that data for a few of the ISB.

After defining the rates in 360 Months buckets and clicking View, the Interest Rate View window displays the result in 360 months view. Here, the Show 360 Months Buckets check box is selected by default.

If you have defined the rates in the ISB and click View, the Interest Rate View window displays the result in the ISB view. Here, the Show 360 Months Buckets check box is disabled by default. On selecting this check box, the results will be displayed for the 360 months view. You cannot enter the values against buckets for this method in 360 months or ISB view.

Use the Excel Import or Export feature to add the interest rates. For more information, see the Excel Import or Export section.

Implied Forward: View U. S. dollar interest rates forecasted from the Treasury Index rates and terms in effect at the as-of date and consistent with the modeling buckets.

From Currency Codes, select USD: US Dollar.
From Interest Rate Codes, select US Treasury Curve.
From Rate Forecast Method, click Implied Forward.
Click Define and enter a shock amount to apply to the IRC in absolute or percentage change. You can designate either absolute rate change or percent rate change. If no change is required to the base curve, leave at 0.0, and click Apply.
Use the Excel Import or Export feature to add the absolute or percent rate changes. For more information, see the Excel Import or Export section.
Click View to view the Implied Forward Rates.

After clicking View, the Interest Rate View window displays the results in the ISB view. Here, Show Rates for Show360 Months Buckets check box is disabled by default. On selecting this check box, the results will be displayed for the 360 months view. You cannot enter the values against buckets for this method in 360 months view. The Show 360 Months Buckets check box is available by default if the ADCo LDM, or Moody's structured cashflow library, or both functions are mapped to you.

Change from Base: Select a Forecast Rate scenario that you have already defined and saved and change it by typing incremental changes to rates. For example, you might want to forecast for a scenario 1 based on incremental changes to the rates in scenario 2.

After clicking View, the Interest Rate View window displays the results in the ISB view. Here, Show Rates for 360 Months Buckets check box is disabled by default. On selecting this check box, the results will be displayed for the 360 months view. You cannot enter the values against buckets for this method in 360 months view. The Show 360 Months Buckets check box is available by default if the ADCo LDM, or Moody's structured cashflow library, or both functions are mapped to you.

Yield Curve Twist: Setting up a scenario to steepen or flatten a given yield curve.

From Currency Codes, select USD: US Dollar.
From Interest Rate Codes, select US Treasury Curve.
From Rate Forecast Method, select Yield Curve Twist.
Click Define.
5. Enter the interest rate changes (flattening the curve around the three-month term point).
Click Apply.

After clicking View, the Interest Rate View window displays the results in the ISB view. Here, Show Rates for Show 360 Months Buckets check box is disabled by default. On selecting this check box, the results will be displayed for the 360 months view. You cannot enter the values against buckets for this method in 360 months view. The Show 360 Months Buckets check box is available by default if the ADCo LDM, or Moody's structured cashflow library, or both functions are mapped to you.

After you have defined the Forecast method for an Interest Rate Code, you can undo the definition by selecting the relevant Interest Rate Code (green color check box) and clicking the Un-Define option. This will bring the Interest Rate Code to its original undefined state indicated by Red Color check box. This step is necessary if you want to delete an Interest Rate Code from the Interest Rates window of the Rate Management window after defining the Forecast method for it.

Standardized Approach Shocks

Note:

Standardized Approach shocks are different than other Interest Rate Rules as these are applied at the scenario level instead of at the IRC level. When you create a new Forecast Rates rule, the default Scenario 1 is always the base scenario for Standardized Approach purposes and cannot have a Standardized Approach shock definition.

In Forecast Rates window, select the IRRBB Shocks. This allows you to define either Standardized or Enhanced Approach Scenarios, or both for a single Forecast Rates Rule. Once a forecast rates rule is designated as IRRBB Shocks, this check box cannot be unselected unless there are no defined scenarios as either Standardized or Enhanced Approach scenario type.
To apply a Standardized Approach scenario, click the Add Scenario.
In the Add Forecast Rates Scenario window, select the Scenario Type to apply the scenario.
Only one Standardized Approach shock can be applied to a single scenario, and no two SA shocks of the same type may be applied to the same Forecast Rates rule. All qualifying IRCs will inherit this SA shock and cannot be changed except for their interpolation method and minimum rate.
Click Apply to make scenario as Standardized Approach shock.

Enhanced Approach Shocks

Like Standardized Approach shocks, Enhanced Approach shocks are scenario-level rules, and Scenario 1 is always referred to as the Base scenario for reporting purposes. However, unlike Standardized Approach shocks, the Forecast method for each IRC is not pre-established. This means that users must define the Forecast method, interpolation method and minimum rate for all Interest Rates in each scenario. Once defined and processed, the results will flow through into the Table B reporting.

In the Forecast Rates window, select the IRRBB Shocks. This allows you to define either Standardized or Enhanced Approach scenarios, or both for a single Forecast Rate rule. After a Forecast Rate rule is designated as IRRBB Shocks, this check box cannot be unselected unless there are no defined scenarios as either Standardized or Enhanced Approach Scenario Type.
To apply an Enhanced Approach scenario, click the Add Scenario.
Only one Enhanced Approach shock can be applied to a single scenario, and no two EA shocks of the same type can be applied to the same Forecast Rates rule. All IRCs in this scenario remain fully editable for the Forecast method, Interpolation method, and Minimum Rate.
Click Apply to make the scenario as Enhanced Approach shock.