Financial Derivatives Toolbox

Interest Rate Term Structure

The Financial Derivatives Toolbox includes a set of functions to encapsulate interest rate term information into a single structure. These functions present a convenient way to package all information related to interest rate terms into a common format, and to resolve interdependencies when one or more of the parameters is modified. For information, see:

• Creation or Modification (intenvset) for a discussion of how to create or modify an interest rate term structure (RateSpec) using the intenvset function.
• Obtaining Specific Properties (intenvget) for a discussion of how to extract specific properties from a RateSpec.

Creation or Modification (intenvset)

The main function to create or modify an interest rate term structure RateSpec (rates specification) is intenvset. If the first argument to this function is a previously created RateSpec, the function modifies the existing rate specification and returns a new one. Otherwise, it creates a new RateSpec. The other intenvset arguments are property-value pairs, indicating the new value for these properties. The properties that can be specified or modified are:

• Compounding
• Disc
• Rates
• EndDates
• StartDates
• ValuationDate
• Basis
• EndMonthRule

To learn about the properties EndMonthRule and Basis, type help ftbEndMonthRule and help ftbBasis or see the Financial Toolbox User's Guide.

Consider again the original table of interest rates.

From	To	Rate
15 Feb 2000	15 Aug 2000	0.05
15 Feb 2000	15 Feb 2001	0.056
15 Feb 2000	15 Aug 2001	0.06
15 Feb 2000	15 Feb 2002	0.065
15 Feb 2000	15 Aug 2002	0.075

Use the information in this table to populate the RateSpec structure.

• StartDates = ['15-Feb-2000'];
  EndDates =   ['15-Aug-2000';
                '15-Feb-2001'; 
                '15-Aug-2001';
                '15-Feb-2002';
                '15-Aug-2002'];
  Compounding = 2;
  ValuationDate = ['15-Feb-2000'];
  Rates = [0.05; 0.056; 0.06; 0.065; 0.075];
  
  rs = intenvset('Compounding',Compounding,'StartDates',... 
  StartDates, 'EndDates', EndDates, 'Rates', Rates,... 
  'ValuationDate', ValuationDate)
  
  rs = 
  
         FinObj:'RateSpec'
    Compounding:2
           Disc:[5x1 double]
          Rates:[5x1 double]
       EndTimes:[5x1 double]
     StartTimes:[5x1 double]
       EndDates:[5x1 double]
     StartDates:730531
  ValuationDate:730531
          Basis: 0
   EndMonthRule: 1
  

Some of the properties filled in the structure were not passed explicitly in the call to RateSpec. The values of the automatically completed properties depend upon the properties that are explicitly passed. Consider for example the StartTimes and EndTimes vectors. Since the StartDates and EndDates vectors are passed in, as well as the ValuationDate, intenvset has all the information needed to calculate StartTimes and EndTimes. Hence, these two properties are read only.

Obtaining Specific Properties (intenvget)

The complementary function to intenvset is intenvget. This function obtains specific properties from the interest rate term structure. The syntax of this function is

• ParameterValue = intenvget(RateSpec, 'ParameterName')
  

To obtain the vector EndTimes from the RateSpec structure, enter

• EndTimes = intenvget(rs, 'EndTimes')
  
  EndTimes =
  
       1
       2
       3
       4
       5
  

To obtain Disc, the values for the discount factors that were calculated automatically by intenvset, type

• Disc = intenvget(rs, 'Disc')
  
  Disc =
  
      0.9756
      0.9463
      0.9151
      0.8799
      0.8319
  

These discount factors correspond to the periods starting from StartDates and ending in EndDates.

Note    Although you can directly access these fields within the structure instead of using intenvget, we strongly advise against this. The format of the interest rate term structure could change in future versions of the toolbox. Should that happen, any code accessing the RateSpec fields directly would stop working.

Now use the RateSpec structure with its functions to examine how changes in specific properties of the interest rate term structure affect those depending upon it. As an exercise, change the value of Compounding from 2 (semiannual) to 1 (annual).

• rs = intenvset(rs, 'Compounding', 1);
  

Since StartTimes and EndTimes are measured in units of periodic discount, a change in Compounding from 2 to 1 redefines the basic unit from semiannual to annual. This means that a period of six months is represented with a value of 0.5, and a period of one year is represented by 1. To obtain the vectors StartTimes and EndTimes, enter

• StartTimes = intenvget(rs, 'StartTimes');
  EndTimes = intenvget(rs, 'EndTimes');
  Times = [StartTimes, EndTimes]
  
  Times =
  
           0    0.5000
           0    1.0000
           0    1.5000
           0    2.0000
           0    2.5000
  

Since all the values in StartDates are the same as the valuation date, all StartTimes values are zero. On the other hand, the values in the EndDates vector are dates separated by six-month periods. Since the redefined value of compounding is 1, EndTimes becomes a sequence of numbers separated by increments of 0.5.

Interest Rate Term Conversions

Pricing and Sensitivity from Interest Rate Term Structure