R: AnnivDates (time-invariant properties and temporal structure)

AnnivDates {BondValuation}

R Documentation

AnnivDates (time-invariant properties and temporal structure)

Description

AnnivDates returns a bond's time-invariant characteristics and temporal structure as a list of three or four named data frames.

Usage

AnnivDates(
  Em = as.Date(NA),
  Mat = as.Date(NA),
  CpY = as.numeric(NA),
  FIPD = as.Date(NA),
  LIPD = as.Date(NA),
  FIAD = as.Date(NA),
  RV = as.numeric(NA),
  Coup = as.numeric(NA),
  DCC = as.numeric(NA),
  EOM = as.numeric(NA),
  DateOrigin = as.Date("1970-01-01"),
  InputCheck = 1,
  FindEOM = FALSE,
  RegCF.equal = 0
)

Arguments

`Em`	The bond's issue date. (required)
`Mat`	Maturity date, i.e. date on which the redemption value and the final interest are paid. (required)
`CpY`	Number of interest payments per year (non-negative integer; element of the set {0,1,2,3,4,6,12}. Default: 2.
`FIPD`	First interest payment date after `Em`.
`LIPD`	Last interest payment date prior to `Mat`.
`FIAD`	Date on which the interest accrual starts (so-called "dated date").
`RV`	The redemption value of the bond. Default: 100.
`Coup`	Nominal interest rate per year in percent. Default: `NA`.
`DCC`	The day count convention the bond follows. Default: `NA`. For a list of day count conventions currently implemented type `View(List.DCC)`.
`EOM`	Boolean indicating whether the bond follows the End-of-Month rule. Default: `NA`.
`DateOrigin`	Determines the starting point for the daycount in "Date" objects. Default: "1970-01-01".
`InputCheck`	If 1, the input variables are checked for the correct format. Default: 1.
`FindEOM`	If `TRUE`, `EOM` is overridden by the value inferred from the data. Default: `FALSE`.
`RegCF.equal`	If 0, the amounts of regular cash flows are calculated according to the stipulated `DCC`. Any other value forces all regular cash flows to be equal sized. Default: 0.

Details

AnnivDates generates a list of the three data frames Warnings, Traits and DateVectors. If the variable Coup is passed to the function, the output contains additionally the data frame PaySched. AnnivDates is meant to analyze large data frames. Therefore some features are implemented to evaluate the quality of the data. The output of these features is stored in the data frame Warnings. Please see section Value for a detailed description of the tests run and the meaning of the variables in Warnings. The data frame Traits contains all time-invariant bond characteristics that were either provided by the user or calculated by the function. The data frame DateVectors contains three vectors of Date-Objects named RealDates, CoupDates and AnnivDates and three vectors of numerics named RD_indexes, CD_indexes and AD_indexes. These vectors are used in the other functions of this package according to the methodology presented in Djatschenko (2018). The data frame PaySched matches CoupDates to the actual amount of interest that the bond pays on the respective interest payment date. Section Value provides further information on the output of the function AnnivDates. Below information on the proper input format is provided. Subsequently follows information on the operating principle of the function AnnivDates and on the assumptions that are met to estimate the points in time needed to evaluate a bond.

The dates Em, Mat, FIPD, LIPD and FIAD can be provided as
1. "Date" with format "%Y-%m-%d", or
2. "numeric" with the appropriate DateOrigin, or
3. number of class "character" with the appropriate DateOrigin, or
4. string of class "character" in the format "yyyy-mm-dd".
CpY, RV and Coup can be provided either as class "numeric" or as a number of class "character".
The provided issue date (Em) is instantly substituted by the first interest accrual date (FIAD) if FIAD is available and different from Em.
Before the determination of the bond's date characteristics begins, the code evaluates the provided calendar dates for plausibility. In this process implausible dates are dropped. The sort of corresponding implausibility is identified and stored in a warning flag. (See section Value for details.)

The remaining valid calendar dates are used to gauge whether the bond follows the End-of-Month-Rule. The resulting parameter est_EOM can take on the following values:

-

*Case 1:*	`FIPD` and `LIPD` are both `NA`
___________	____________________________________
`est_EOM = 1`	, if `Mat` is the last day of a month.
`est_EOM = 0`	, else.
==========	================================

-

*Case 2:*	`FIPD` is `NA` and `LIPD` is a valid calendar date
___________	____________________________________
`est_EOM = 1`	, if `LIPD` is the last day of a month.
`est_EOM = 0`	, else.
==========	================================

-

*Case 3:*	`FIPD` is a valid calendar date and `LIPD` is `NA`
___________	____________________________________
`est_EOM = 1`	, if `FIPD` is the last day of a month.
`est_EOM = 0`	, else.
==========	================================

-

*Case 4:*	`FIPD` and `LIPD` are valid calendar dates
___________	____________________________________
`est_EOM = 1`	, if `LIPD` is the last day of a month.
`est_EOM = 0`	, else.
==========	================================

If EOM is initially missing or NA or not element of {0,1}, EOM is set est_EOM with a warning.

If the initially provided value of EOM deviates from est_EOM, the following two cases apply:

________	_________________________________________
Case 1:	If `EOM = 0` and `est_EOM = 1`:
	`EOM` is not overridden and remains `EOM = 0`
________	_________________________________________
Case 2:	If `EOM = 1` and `est_EOM = 0`:
	`EOM` is overridden and set `EOM = 0` with a warning.
	Keeping `EOM = 1` in this case would conflict with
	the provided `Mat`, `FIPD` or `LIPD`.
________	_________________________________________
Note:	Set the option `FindEOM=TRUE` to always use
	`est_EOM` found by the code.
=======	====================================

If FIPD and LIPD are both available, the lengths of the first and final coupon periods are determinate and can be "regular", "long" or "short". To find the interest payment dates between FIPD and LIPD the following assumptions are met:
1. ```
The interest payment dates between FIPD and LIPD are
  evenly distributed.
```
2. ```
The value of EOM determines the location of
  all interest payment dates.
```
If assumption 1 is violated, the exact locatations of the interest payment dates between FIPD and LIPD are ambiguous. The assumption is violated particularly, if
1. FIPD and LIPD are in the same month of the same year but not on the same day, or
2. the month difference between FIPD and LIPD is not a multiple of the number of months implied by CpY, or
3. FIPD and LIPD are not both last day in month, their day figures differ and the day figure difference between FIPD and LIPD is not due to different month lengths.
In each of the three cases, FIPD and LIPD are dropped with the flag IPD_CpY_Corrupt = 1.
If neither FIPD nor LIPD are available the code evaluates the bond based only upon the required variables Em and Mat (and CpY, which is 2 by default). Since FIPD is not given, it is impossible to distinguish between a "short" and "long" odd first coupon period, without an assumption on the number of interest payment dates. Consequently the first coupon period is assumed to be either "regular" or "short". The locations of FIPD and LIPD are estimated under the following assumptions:
1. ```
The final coupon period is "regular".
```
2. ```
The interest payment dates between the estimated
  FIPD and Mat are evenly distributed.
```
3. ```
The value of EOM determines the location of
  all interest payment dates.
```
If LIPD is available but FIPD is not, the length of the final coupon payment period is determined by LIPD and Mat and can be "regular", "long" or "short". The locations of the interest payment dates are estimated under the following assumptions:
1. ```
The first coupon period is either "regular" or "short".
```
2. ```
The interest payment dates between the estimated
  FIPD and LIPD are evenly distributed.
```
3. ```
The value of EOM determines the location of
  all interest payment dates.
```
If FIPD is available but LIPD is not, the length of the first coupon payment period is determined by Em and FIPD and can be "regular", "long" or "short". The locations of the interest payment dates are estimated under the following assumptions:
1. ```
The final coupon period is either "regular" or "short".
```
2. ```
The interest payment dates between FIPD and
  the estimated LIPD are evenly distributed.
```
3. ```
The value of EOM determines the location of
  all interest payment dates.
```

Value

All dates are returned irrespective of whether they are on a business day or not.

DateVectors (data frame)

-
RealDates: A vector of Date class objects with format "%Y-%m-%d" in ascending order, that contains the issue date, all actual coupon payment dates and the maturity date.
RD_indexes: A vector of numerics capturing the temporal structure of the bond.
CoupDates: A vector of Date class objects with format "%Y-%m-%d" in ascending order, that contains all actual coupon payment dates and the maturity date.
CD_indexes: A vector of numerics capturing the temporal structure of the bond.
AnnivDates: A vector of Date class objects with format "%Y-%m-%d" in ascending order, that contains all theoretical coupon anniversary dates. The first value of AnnivDates is the anniversary date immediately preceding the issue date, if the bond has an irregular first coupon period; otherwise it is the issue date. The final value of AnnivDates is the anniversary date immediately succeeding the maturity date, if the bond has an irregular final coupon period; otherwise it is the maturity date.
AD_indexes: A vector of numerics capturing the temporal structure of the bond.
-

PaySched (data frame)

-
CoupDates: A vector of Date class objects with format "%Y-%m-%d" in ascending order, that contains all actual coupon payment dates and the maturity date.
CoupPayments: A vector of class "numeric" objects, that contains the actual amounts of interest that the bond pays on the respective coupon payment dates. The unit of these payments is the same as that of RV that was passed to the function. RV is not included in the final interest payment.
NOTE:: PaySched is created only if the variable Coup is provided.
-

Traits (data frame)

-
DateOrigin: The starting point for the daycount in "Date" objects.
CpY: Number of interest payments per year.
FIAD: Date on which the interest accrual starts (so-called "dated date").
Em: The bond's issue date that was used for calculations.
Em_Orig: The bond's issue date that was entered.
FIPD: The first interest payment date after Em that was used for calculations. If the entered FIPD was dropped during the calculation process, the value is NA.
FIPD_Orig: The first interest payment date after Em that was entered.
est_FIPD: The estimated first interest payment date after Em. NA, if a valid FIPD was entered.
LIPD: The last interest payment date prior to Mat that was used for calculations. If the entered LIPD was dropped during the calculation process, the value is NA.
LIPD_Orig: The last interest payment date prior to Mat that was entered.
est_LIPD: The estimated last interest payment date prior to Mat. NA, if a valid LIPD was entered.
Mat: The maturity date that was entered.
Refer: Reference date that determines the day figures of all AnnivDates.
FCPType: A character string indicating the type of the first coupon period. Values: "long", "regular", "short".
FCPLength: Length of the first coupon period as a fraction of a regular coupon period.
LCPType: A character string indicating the type of the last coupon period. Values: "long", "regular", "short".
LCPLength: Length of the final coupon period as a fraction of a regular coupon period.
Par: The redemption value of the bond.
CouponInPercent.p.a: Nominal interest rate per year in percent.
DayCountConvention: The day count convention the bond follows.
EOM_Orig: The value of EOM that was entered.
est_EOM: The estimated value of EOM.
EOM_used: The value of EOM that was used in the calculations.
-

Warnings (data frame)

-

A set of flags that indicate the occurrence of warnings during the execution. Below they are listed according to the hierarchical structure within the function AnnivDates.

-




*Em_FIAD_differ* =
1		, if the provided issue date (`Em`) was substituted by the first
		interest accrual date (`FIAD`).
		This happens, if `FIAD` is available and different from `Em`.
		________________________________________________
		Note: No warning is displayed.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*EmMatMissing* =
1		, if either issue date (`Em`) or maturity date (`Mat`) or both
		are missing or `NA`.
		________________________________________________
		Output: RealDates `= NA`, CoupDates `= NA`,
		AnnivDates `= NA`, FCPType `= NA`, LCPType `= NA`.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*CpYOverride* =
1		, if number of interest periods per year (`CpY`) is missing or
		`NA`, or if the provided `CpY` is not element of {0,1,2,3,4,6,12}.
		________________________________________________
		Note: `CpY` is set 2, and the execution continues.
		________________________________________________
		Output: as if `CpY` = 2 was provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*RV_set100percent* =
1		, if the redemption value (`RV`) is missing or `NA`.
		________________________________________________
		Note: `RV` is set 100, and the execution continues.
		________________________________________________
		Output: as if `RV` = 100 was provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*NegLifeFlag* =
1		, if the provided maturity date (`Mat`) is before or on the
		provided issue date (`Em`).
		________________________________________________
		Output: RealDates `= NA`, CoupDates `= NA`,
		AnnivDates `= NA`, FCPType `= NA`, LCPType `= NA`.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*ZeroFlag* =
1		, if number of interest payments per year (`CpY`) is `0`.
		________________________________________________
		Output: RealDates `= (Em,Mat)`, CoupDates `= Mat`,
		AnnivDates `= (Em,Mat)`, FCPType `= NA`, LCPType `= NA`.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*Em_Mat_SameMY* =
1		, if the issue date (`Em`) and the maturity date (`Mat`) are in the
		same month of the same year but not on the same day, while
		`CpY` is an element of {1,2,3,4,6,12}.
		________________________________________________
		Output: RealDates `= (Em,Mat)`, CoupDates `= Mat`,
		FCPType `= short`, LCPType `= short`.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*ChronErrorFlag* =
1		, if the provided dates are in a wrong chronological order.
		________________________________________________
		Note:
		The correct ascending chronological order is:
		issue date (`Em`), first interest payment date (`FIPD`),
		last interest payment date (`LIPD`), maturity date (`Mat`).
		`FIPD` and `LIPD` are set `as.Date(NA)`.
		________________________________________________
		Output: as if `FIPD` and `LIPD` were not provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*FIPD_LIPD_equal* =
1		if `Em` < `FIPD` = `LIPD` < `Mat`.
		________________________________________________
		Output: AnnivDates contains `FIPD` and has at least `3` elements.
		RealDates `= (Em,FIPD,Mat)`, CoupDates `= (FIPD,Mat)`.
		FCPType and LCPType can be "short", "regular" or "long".
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*IPD_CpY_Corrupt* =
1		, if the provided first interest payment date (`FIPD`) and last
		interest payment date (`LIPD`) are inconsistent with the
		provided number of interest payments per year (`CpY`).
		________________________________________________
		Note:
		Inconsistency occurs if
		1. `FIPD` and `LIPD` are in the same month of the same year
		but not on the same day, or
		2. the number of months between `FIPD` and `LIPD` is not a
		multiple of the number of months implied by `CpY`, or
		3. `FIPD` and `LIPD` are not both last day in month, their
		day figures differ and the day figure difference between
		`FIPD` and `LIPD` is not due to different month lengths.

		In each of the three cases keeping the provided values of
		`FIPD` and `LIPD` would violate the assumption, that the
		anniversary dates between `FIPD` and `LIPD` are evenly
		distributed.
		________________________________________________
		`FIPD` and `LIPD` are set `as.Date(NA)`
		and the execution continues.
		________________________________________________
		Output:
		as if `FIPD` and `LIPD` were not provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*EOM_Deviation* =
1		, if the provided value of `EOM` deviates from the value that
		is inferred from the provided calendar dates.
		________________________________________________
		Note:
		The program analyses the valid values of `Em`, `Mat`, `FIPD` and
		`LIPD` to determine the appropriate value of `EOM`.

		If the initially provided value of `EOM` deviates from the value
		determined by the program, there might be an inconsistency
		in the provided data.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*EOMOverride* =
1		, if the provided value of `EOM` is overridden by a value that
		is inferred from the provided calendar dates.
		________________________________________________
		Note:
		This happens automatically if `EOM` is initially missing or `NA`
		or not element of `{0,1}` and if the provided value of `EOM`
		conflicts with the provided values of `FIPD`, `LIPD` or `Mat`,
		e.g. if `est_EOM = 0` but `EOM = 1`.
		If `EOM_Deviation = 1` and the option `FindEOM` is set `TRUE`,
		the initially provided value of `EOM` is also overridden by the
		value that is inferred from the provided calendar dates if
		`est_EOM = 1` but `EOM = 0`.
		________________________________________________
		Output:
		as if the value of `EOM` that is found by the program was
		provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*DCCOverride* =
1		if `DCC` is missing or NA or not element of c(1:16).
		________________________________________________
		Note:
		If the program cannot process the provided day count
		identifier `DCC`, it overrides it with `DCC` = 2.
		________________________________________________
		Output:
		as if `DCC` = 2 was provided initially.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

-

*NoCoups* =
1		, if there are no coupon payments between the provided
		issue date (`Em`) and the maturity date (`Mat`), but the
		provided (`CpY`) is not zero.
		________________________________________________
		Output:
		RealDates `= (Em,Mat)`, CoupDates `= (Mat)`,
		AnnivDates contains `Mat` and has either
		`2` or `3` elements, FCPType = LCPType and
		can be `"short"`, `"regular"` or `"long"`.
___________________	___	________________________________________________
0		, else.
=================	===	===========================================

References

Djatschenko, Wadim, The Nitty Gritty of Bond Valuation: A Generalized Methodology for Fixed Coupon Bond Analysis Allowing for Irregular Periods and Various Day Count Conventions (November 5, 2018). Available at SSRN: https://ssrn.com/abstract=3205167.

Examples

data(SomeBonds2016)

# Applying the function AnnivDates to the data frame SomeBonds2016.
system.time(
  FullAnalysis<-apply(SomeBonds2016[,c('Issue.Date','Mat.Date','CpY.Input','FIPD.Input',
  'LIPD.Input','FIAD.Input','RV.Input','Coup.Input','DCC.Input','EOM.Input')],1,function(y)
  AnnivDates(y[1],y[2],y[3],y[4],y[5],y[6],y[7],y[8],y[9],y[10],RegCF.equal=1)),
gcFirst = TRUE)
# warnings are due to apply's conversion of the variables' classes in
# SomeBonds2016 to class "character"

# The output stored in FullAnalysis ist a nested list.
# Lets look at what is stored in FullAnalysis for a random bond:
randombond<-sample(c(1:nrow(SomeBonds2016)),1)
FullAnalysis[[randombond]]

# Extracting the data frame Warnings:
AllWarnings<-do.call(rbind,lapply(FullAnalysis, `[[`, 1))
summary(AllWarnings)
# binding the Warnings to the bonds
BondsWithWarnings<-cbind(SomeBonds2016,AllWarnings)

# Extracting the data frame Traits:
AllTraits<-do.call(rbind,lapply(FullAnalysis, `[[`, 2))
summary(AllTraits)
# binding the Traits to the bonds
BondsWithTraits<-cbind(SomeBonds2016,AllTraits)

# Extracting the data frame AnnivDates:
AnnivDates<-lapply(lapply(FullAnalysis, `[[`, 3), `[[`, 5)
AnnivDates<-lapply(AnnivDates, `length<-`, max(lengths(AnnivDates)))
AnnivDates<-as.data.frame(do.call(rbind, AnnivDates))
AnnivDates<-as.data.frame(lapply(AnnivDates, as.Date, as.Date(AllTraits$DateOrigin[1])))
# binding the AnnivDates to the bonds:
BondsWithAnnivDates<-cbind(SomeBonds2016,AnnivDates)

# Extracting the data frames PaySched for each bond and creating a panel:
CoupSched<-lapply(FullAnalysis, `[[`, 4)
CoupSchedPanel<-SomeBonds2016[rep(row.names(SomeBonds2016),sapply(CoupSched, nrow)),]
CoupSched<-as.data.frame(do.call(rbind, CoupSched))
CoupSchedPanel<-cbind(CoupSchedPanel,CoupSched)

[Package BondValuation version 0.1.1 Index]