Day Count Methods

In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements. This determines the number of days between two coupon payments; thus, calculating the amount transferred on payment dates and also the accrued interest for dates between payments. The day count is also used to quantify periods of time when discounting a cash-flow to its present value. When a security such as a bond is sold between interest payments dates, the seller is eligible to some fraction of the coupon amount. It should be noted that the day count convention is also used in many other formulas in financial mathematics as well. - Wikipedia

Note: When determining which day count method to use one should take great caution as the methods are known by many names and depending upon the market or context the names may be ambiguous. One should always review the algorithm description to insure that they are using the correct method.

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Actual 360

This convention is used in money markets for short-term lending currencies, including US dollar and Euro, and is applied in ESCB monetary policy operations. Additionally, it is the convention used with Repurchase agreements.

Calculation Method Summary:

Factor = Days(Date1 , Date2) / 360

where the function Days(d1, d2) represents the number of days between Date1 and Date2.

Also known as:

• Actual/360
• Act/360
• A/360
• French

References:

• ICMA Rule 251.1(i) not sterling
• ISDA 2006 Section 4.1.6(e)
• (Mayle 1993)

Usage:

val d1 = Date(31, 1, 1990)
val d2 = Date(16, 3, 1991)
val yf : Double = Actual360().yearFraction(d1, d2)

such that yf rounded to the 9th position = 1.136111111

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Actual 365F

Calculation Method Summary:

Factor = Days(Date1 , Date2) / 365

where the function Days(d1, d2) represents the number of days between Date1 and Date2.

Also known as:

• Act/365 Fixed
• A/365 Fixed
• A365F
• English

Sources: ISDA 2006 Section 4.1.6(d)

Usage:

val d1 = Date(31, 1, 1990)
val d2 = Date(16, 3, 1991)
val yf : Double = Actual365Fixed().yearFraction(d1, d2)

such that yf rounded to the 9th position = 1.120547945

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Actual Actual

The convention of this class calculate the number of days between two dates as the Julian difference.

Actual/Actual ISMA

Calculation Method Summary:

Factor = Days(Date1 , Date2) / Freq * Days(Date1, Date3)

Also known as:

• Actual/Actual
• Actual/Actual ICMA
• Act/Act ICMA
• ISMA-99
• Act/Act ISMA
• ISMA
• BOND
• ACT/ACT

References:

• ICMA Rule 251.1(iii)
• ISDA 2006 Section 4.1.6(c)
• Mayle 1993
• Actual/Actual comparison, EMU and Market Conventions: Recent Developments

Usage:

val d1 = new Date(1, 11, 2003)
val d2 = new Date(1, 5, 2004)

val d3 = new Date(1, 11, 2003)
val d4 = new Date(1, 5, 2004)


val yf :Double = ActualActual(ISMA).yearFraction(d1, d2, d3, d4)

assert(yf.rounded(9) == 0.500000000)

such that yf1 rounded to the 9th position = 0.500000000

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Actual/Actual ISDA

Calculation Method Summary:

Factor = (Days not in leap year / 365) + (Days in leap year / 366)

Also known as:

• Actual/Actual
• Act/Act
• Actual/365
• Act/365
• ISDA
• HISTORICAL
• ACTUAL365

References:

ISDA 2006 Section 4.16(b)

Usage:

val d1 = Date(31, 1, 1990)
val d2 = Date(16, 3, 1991)

val yf : Double = ActualActual(ISDA).yearFraction(d1, d2)

such that yf rounded to the 9 position =   1.120547945

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Actual/Actual AFB

Calculation Method Summary:

This convention requires a set of rules in order to determine the number of days in a year. The basic rule is that if February 29 is in the range from date1 (inclusive) to date2 (exclusive) then days in year = 365.

If the period from date1 to date2 is more than one year, the calculation is split into two parts. The first part is the number of complete years, counted back from the last day of the period. The second part is the remaining initial stub, calculated using the basic rule.

Also known as:

• Actual/Actual AFB
• AFB
• EURO

Sources:

• "Definitions Communes plusieurs Additifs Techniques", by the Association Francaise des Banques in September 1994.[8]
• FBF Master Agreement for Financial Transactions, Supplement to the Derivatives Annex, Edition 2004, section 7i.[9]
• Actual/Actual comparison, EMU and Market Conventions: Recent Developments

Usage:

val d1 = Date(31, 1, 1990)
val d2 = Date(16, 3, 1991)

val yf : Double = ActualActual(AFB).yearFraction(d1, d2)

such that yf rounded to the 9th place =  1.120547945

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Business 252

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Thirty 360