"30/360" - Rules Expressed Differently

Q

What are different ways to express "30/360" Day Count Rules?

✍: FYIcenter.com

A

Many web sites express the 30/360 Day Count Convention rules differently, and name it differently. But if you can prove that they are all specifying the same rules.

cbonds.com

Names: 30/360 ISDA, 30/360, Bond Basis, 30-360 U.S. Municipal

Rules: 
  Day count = (Y2-Y1)·360 + (M2-M1)·30 + (D2-D1)

  Convention:
  • if D1=31 then D1=30
  • if D2=31 and D1=30 or 31 then D2=30

isda.org

Names: 30/360, 360/360, Bond Basis

Rules: 
  Day Count Fraction = (360*(Y2-Y1) + 30*(M2-M1) + (D2-D1)) / 360

  where:
  - “D1” is the first calendar day, expressed as a number, of the 
    Calculation Period or Compounding Period, unless such number 
    would be 31, in which case D1 will be 30;
  - “D2” is the calendar day, expressed as a number, immediately 
    following the last day included in the Calculation Period or 
    Compounding Period, unless such number would be 31 and D1 is 
    greater than 29, in which case D2 will be 30;

opengamma.io

Names: 30/360 ISDA, 30/360 U.S. Municipal, 30/360 Bond Basis

Rules: 
  result = (360 * deltaYear + 30 * deltaMonth + deltaDay) / 360

  The deltaDay is then calculated once day-of-month adjustments have
  occurred:
  - If the second day-of-month is 31 and the first day-of-month 
    is 30 or 31, change the second day-of-month to 30.
  - If the first day-of-month is 31, change the first day-of-month 
    to 30.

Wadim Djatschenko: The Nitty Gritty of Bond Valuation

Names: 30/360

Rules: 
  DIST(T1,T2) = (360*(Y2-Y1) + 30*(M2-M1) + (D2-D1)) / 360

  The adjustment rules can be summarized as:
  - D1 = min(30, D1)
  - D2 = 30, if D2 = 31 and (D1 = 30 or 31)

wikipedia.org

Names: 30/360 Bond Basis, 30A/360

Rules: 
  DayCountFactor = (360*(Y2-Y1) + 30*(M2-M1) + (D2-D1)) / 360

  Date adjustment rules:
    D1 = min(D1, 30), 
    If D1 > 29 then D2 = min(D2, 30) 

The best way to specify the 30/360 convention rules is:

  T1 = (Y1,M1,D1)
  T2 = (Y2,M2,D2)
  Day_Count_Factor = (360*(Y2-Y1) + 30*(M2-M1) + (D2-D1)) / 360 

  where D1 and D2 are adjusted as below:
    If D1 = 31, set D1 = 30;
    If D2 = 31 and D1 > 29, set D2 = 30.

 

"30/360" - Day Count Examples by ISDA

What Is "30/360"

Day Count Convention - "30/360"

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