Discount factors from interest rates (2024)

Table of Contents
Syntax Description Examples Compute Discount Factors From Interest Rates Input Arguments Compounding — Compounding rate integer with value of 0, 1, 2, 3, 4, 6, 12, 365, -1 Rates — Rates decimal EndTimes — End times serial date number | date character vector | numeric StartTimes — Start times serial date number | date character vector | numeric ValuationDate — Observation date of the investment horizons entered in StartTimes and EndTimesserial date number | date character vector Basis — Day-count basis 0 (actual/actual) (default) | integer from 0 to 13 EndMonthRule — End-of-month rule flag 1 (in effect) (default) | nonnegative integer with values 0 or 1 Output Arguments Disc — Discount factors vector EndTimes — Times ending the interval to discount over vector StartTimes — Times starting the interval to discount over vector Version History See Also Topics Open Example MATLAB Command Americas Europe Asia Pacific

Discount factors from interest rates

collapse all in page

Syntax

Disc = rate2disc(Compounding,Rates,EndTimes,StartTimes)

[Disc,EndTimes,StartTimes] = rate2disc(Compounding,Rates,EndTimes,StartTimes,ValuationDate,Basis,EndMonthRule)

Description

example

Disc = rate2disc(Compounding,Rates,EndTimes,StartTimes) computes discount factors from interest rates where interval points are input as times in periodic units.

The rate2disc function computes the discounts over a series of NPOINTS time intervals given the annualized yield over those intervals. NCURVES different rate curves can be translated at once if they have the same time structure. The time intervals can represent a zero curve or a forward curve.

The output Disc is an NPOINTS-by-NCURVES column vector of discount factors in decimal form representing the value at time StartTimes of a unit cash flow received at time EndTimes.

example

[Disc,EndTimes,StartTimes] = rate2disc(Compounding,Rates,EndTimes,StartTimes,ValuationDate,Basis,EndMonthRule) computes discount factors from interest rates where ValuationDate is passed and interval points are input as dates.

You can specify the investment intervals either with input times or with input dates. Entering ValuationDate invokes the date interpretation; omitting ValuationDate invokes the default time interpretations.

Examples

collapse all

Compute Discount Factors From Interest Rates

Open Live Script

This example shows the two uses of rate2disc.

Interval Points Are Input as Times in Periodic Units

Compute discounts from a zero curve at 6 months, 12 months, and 24 months. The times to the cash flows are 1, 2, and 4. Use rate2disc to compute the present value (at time 0) of the cash flows.

Compounding = 2;Rates = [0.05; 0.06; 0.065];EndTimes = [1; 2; 4];Disc = rate2disc(Compounding, Rates, EndTimes)
Disc = 3×1 0.9756 0.9426 0.8799

Interval Points Are Input as Dates

Compute discounts from a zero curve at 6 months, 12 months, and 24 months. Use dates to specify the ending time horizon.

Compounding = 2;Rates = [0.05; 0.06; 0.065];EndDates = ['10/15/97'; '04/15/98'; '04/15/99'];ValuationDate = '4/15/97'; Disc = rate2disc(Compounding, Rates, EndDates, [], ValuationDate)
See Also
Interest Rate | Brilliant Math & Science Wiki9.6: Equivalent and Effective Interest Rates9.5: Determining the Interest Rate1.7 Effective and Equivalent Interest Rates – Financial Math – Math 1175
Disc = 3×1 0.9756 0.9426 0.8799

Input Arguments

collapse all

Compounding — Compounding rate
integer with value of 0, 1, 2, 3, 4, 6, 12, 365, -1

Compounding rate for which the input zero rates are compounded when annualized, specified as one of the following scalar integers. Compounding determines the formula for the discount factors (Disc):

  • If Compounding = 0 for simple interest:

    • Disc = 1/(1 + Z * T), where T is time in years and simple interest assumes annual times F = 1.

  • If Compounding = 1, 2, 3, 4, 6, 12:

    • Disc = (1 + Z/F)^(-T), where F is the compounding frequency, Z is the zero rate, and T is the time in periodic units, for example, T = F is one year.

  • If Compounding = 365:

    • Disc = (1 + Z/F)^(-T), where F is the number of days in the basis year and T is a number of days elapsed computed by basis.

  • If Compounding = -1:

    • Disc = exp(-T*Z), where T is time in years.

Data Types: double

Rates — Rates
decimal

Rates, specified as a number of points (NPOINTS) by number of curves (NCURVES) matrix of rates in decimal form. Rates are the yields over investment intervals from StartTimes, when the cash flow is valued, to EndTimes, when the cash flow is received. For example, 5% is 0.05 in Rates.

Data Types: double

EndTimes — End times
serial date number | date character vector | numeric

End times, specified as a scalar or an NPOINTS-by-1 column vector using serial date numbers or date character vectors, or with times in periodic units ending the interval to discount over. When EndTimes is not a date, the value for EndTimes is T computed from SIA semi-annual time factors, Tsemi, by the formula T = Tsemi/2 * F, where F is the compounding frequency. F is set to 1 for continuous compounding.

Note

When ValuationDate is not passed, EndTimes is interpreted as times. If Compounding = 365 (daily), EndTimes is measured in days.

Data Types: double | char

StartTimes — Start times
serial date number | date character vector | numeric

Start times, specified a scalar or an NPOINTS-by-1 column vector using serial date numbers or date character vectors, or with times in periodic units starting the interval to discount over. StartDates must be earlier than EndDates. When StarTimes is not a date, the value for StartTimes is T computed from SIA semi-annual time factors, Tsemi, by the formula T = Tsemi/2 * F, where F is the compounding frequency. F is set to 1 for continuous compounding.

Note

When ValuationDate is not passed, StartTimes is interpreted as times. If Compounding = 365 (daily), StartTimes is measured in days.

Data Types: double | char

ValuationDate — Observation date of the investment horizons entered in StartTimes and EndTimes
serial date number | date character vector

Observation date of the investment horizons entered in StartTimes and EndTimes, specified as scalar serial date number or date character vector.

Note

You can specify the investment intervals either with input times or with input dates. Entering ValuationDate invokes the date interpretation; omitting ValuationDate invokes the default time interpretations.

Data Types: double | char

Basis — Day-count basis
0 (actual/actual) (default) | integer from 0 to 13

Day-count basis of the instrument when using dates for StartTimes and EndTimes, specified as a scalar or an NINST-by-1 vector of integers..

  • 0=actual/actual

  • 1=30/360 (SIA)

  • 2=actual/360

  • 3=actual/365

  • 4=30/360(PSA)

  • 5=30/360(ISDA)

  • 6=30/360(European)

  • 7=actual/365(Japanese)

  • 8=actual/actual (ICMA)

  • 9=actual/360 (ICMA)

  • 10=actual/365 (ICMA)

  • 11=30/360E (ICMA)

  • 12=actual/365 (ISDA)

  • 13=BUS/252

For more information, see Basis.

Data Types: double

EndMonthRule — End-of-month rule flag
1 (in effect) (default) | nonnegative integer with values 0 or 1

End-of-month rule flag when using dates for StartTimes and EndTimes, specified as a scalar or an NINST-by-1 vector of nonnegative integers. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.

  • 0 = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: double

Output Arguments

collapse all

Disc — Discount factors
vector

Discount factors, returned as an NPOINTS-by-NCURVES column vector of in decimal form representing the value at time StartTimes of a unit cash flow received at time EndTimes.

EndTimes — Times ending the interval to discount over
vector

Times ending the interval to discount over, returned as an NPOINTS-by-1 column vector, measured in periodic units.

StartTimes — Times starting the interval to discount over
vector

Times starting the interval to discount over, returned as an NPOINTS-by-1 column vector, measured in periodic units.

Version History

Introduced before R2006a

See Also

disc2rate | ratetimes

Topics

  • Modeling the Interest-Rate Term Structure
  • Interest-Rate Term Conversions
  • Interest Rates Versus Discount Factors
  • Understanding the Interest-Rate Term Structure

Open Example

You have a modified version of this example. Do you want to open this example with your edits?

MATLAB Command

You clicked a link that corresponds to this MATLAB command: 

 
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
 
 
 
 
 
 
 
 Discount factors from interest rates (1) 
 
 
 
 
Select a Web Site
 
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
 
 
 
You can also select a web site from the following list:
 
 
 
Americas
 
     
  • América Latina (Español)
    •  
  • Canada (English)
    •  
  • United States (English)
    •  
 
 
 
Europe
 
 
 
     
  • Belgium (English)
    •  
  • Denmark (English)
    •  
  • Deutschland (Deutsch)
    •  
  • España (Español)
    •  
  • Finland (English)
    •  
  • France (Français)
    •  
  • Ireland (English)
    •  
  • Italia (Italiano)
    •  
  • Luxembourg (English)
    •  
 
 
 
     
  • Netherlands (English)
    •  
  • Norway (English)
    •  
  • Österreich (Deutsch)
    •  
  • Portugal (English)
    •  
  • Sweden (English)
    •  
  • Switzerland 
       
    • Deutsch
      •  
    • English
      •  
    • Français
      •  
     
    •  
  • United Kingdom (English)
    •  
 
 
 
 
 
Asia Pacific
  
 
 
Contact your local office
 
 
 
 
 

                                                        Discount factors from interest rates (2024)
                        

                            
                        

                    

                                                                                                            
Top Articles

                            

                                                                    



    
    

        The 10 Countries with the Most Beautiful Women
    


                                                                    



    
    

        The Remarkable Things A Hug Can Do - Hey Sigmund
    


                                                                                                    



    
    

        RS: The Beach Event is Back and More AFK-Friendly!
    


                



    
    

        The Beach Is Here! - This Week In RuneScape - Lunagang
    


                



    
    

        Best Character Builds in Project Zomboid [Final guide You will need]
    


                



    
    

        [Top 5] Project Zomboid Best Character Builds That Are Powerful
    


                



    
    

        Human Resource Policies in Texas Health Resources | Free Essay
    


                



    
    

        Texas Health and Human Services jobs - Jora
    


                



    
    

        Craigslist Texas Mcallen
    


                



    
    

        Pay Property Taxes Lake County Illinois
    


                



    
    

        WRANGLER Texas Slim | Die schlanke Jeansform
    


                



    
    

        Luther and Other Leaders of the Reformation -
        Christian Classics Ethereal Library
    


                                                                

                                                                
Latest Posts

                        

                                                            



    
    

        A beginner's guide to ISO in photography
    


                                                            



    
    

        Inorganic Fertilizer Advantages and Disadvantages
    


                                                    

                    
                    

        

    
    
    



                    

    
Article information

    
Author:  Jerrold Considine 

    
Last Updated:   

    
Views: 5604

    
Rating: 4.8 / 5 (58 voted)

    
Reviews: 89% of readers found this page helpful





    
Author information

    
Name: Jerrold Considine

    
Birthday: 1993-11-03

    
Address: Suite 447 3463 Marybelle Circles, New Marlin, AL 20765

    
Phone: +5816749283868

    
Job: Sales Executive

    
Hobby: Air sports, Sand art, Electronics, LARPing, Baseball, Book restoration, Puzzles

    
Introduction: My name is Jerrold Considine, I am a combative, cheerful, encouraging, happy, enthusiastic, funny, kind person who loves writing and wants to share my knowledge and understanding with you.