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fixedincome

Classes

  • SpotRate
  • ForwardRate
  • SpotRateCurve
  • Term
  • Compounding
  • Daycount
  • Interpolation

TODO

Documentation

  • Term
  • Compounding
    • Compounding Methods
  • Daycount
  • SpotRate
  • SpotRateCurve
  • ForwardCurve
  • Interpolation

Term

  • work with different units: terms(c(1, 6, 1, 2), c("months", "months", "years", "years"))

Daycount

SpotRate

  • compound and discount functions accept (character, character) date arguments discount(r, "2017-08-01", "2017-08-21")

SpotRateCurve

  • A spotrate should be removed from a spotratecurve: curve[-10] - curve[-n] should return a spotratecurve without the removed spotrate
  • spotratecurve indexing:
    • positional indexing: curve[1] for the first term, curve[2] for the second and so on. If the given index exceeds the curve length this operation returns NA.
    • replacement with positional index curve[1] \<- 0.01
    • associative indexing curve[["1 day"]] for 1 day, curve[["2 days"]] for 2 days, ...
    • If the spotratecurve doesn't have a 2 days index it returns NA
    • removal of associative index
    • replacement with associative index
    • date indexes
      • select
      • remove
      • replace
    • term indexes
      • select
      • remove
      • replace
    • sum curve to: numeric, curve
    • append SpotRateCurve
    • concatenate SpotRateCurve
  • Naming: SpotRateCurve should have a name? I am not sure about that!
  • create DiscountCurve - interpolations should be applied to it.
  • arithmetic operations between curves respecting terms
  • accept terms with different units: terms(c(1, 6, 1, 2), c("months", "months", "years", "years"))

Multi SpotRateCurve

  • Data structure for multiple SpotRateCurve objects, like a matrix. Useful for historical data and to build historical risk factors.

ForwardRate

  • create forward rates
  • daily forward rates with interpolated data
  • create a method for daily forward rates with interpolated data

Interpolation

  • set interpolation to SpotRateCurve
  • unset interpolation to SpotRateCurve
  • Interpolation will be used with associative indexing. If interpolation is set and a missing index is passed, then this value is interpolated.
  • Methods
    • FlatForward
    • Linear
    • LogLinear
    • Monotone Cubic Spline (Hyman)
    • Hermite
    • Natural Spline
    • Nelson-Siegel
    • Nelson-Siegel-Svensson
    • FlatForward COPOM
    • Constrained Spline
    • Dynamic Nelson-Siegel ref1, ref2
    • Vasicek (Haug 11.4.2) ref
    • Rendleman and Bartter (Haug 11.4.1)
    • Ho and Lee (Haug 11.4.3)
    • Hull and White (Haug 11.4.4)
    • Black-Derman-Toy (Haug 11.4.5)
  • Improve curve fit stop using object copy
  • Work with terms in different units

Bonds

  • define bonds
  • pricing bonds

Bootstrap

  • bonds bootstrap
  • Curve models: Nelson-Siegel, Diebold-Li, Nelson-Siegel-Svensson

Other classes

  • IndexCurve - for inflation index or IDI index, for example - rbcb integration
  • HistoricalRates - for CDI historical data, for example - rbcb integration

Plotting

  • SpotRateCurve: points and lines
  • SpotRateCurve: lines with daily interpolated points
  • ForwardRate curve with steps
  • daily ForwardRate curve with interpolated points
  • plot multiple SpotRateCurve objects
  • use daycount to create x-axis ticks

Other issues

Register

  • naming objects and register (aka container)
    • Objects like HistoricalRates, SpotRateCurve, IndexCurve and Calendar should be referenced by their names. These objects are used by many others and their copies should imply unnecessary memory use.
    • Integrate with rbcb package to transform series into IndexCurve or HistoricalRates.
    • Methods which work with these objects should work with characters that represent the objects.

Legacy

Methods to be implemented in the term class:

  • initialize
  • show
  • format.S3
  • xtfrm.S3
  • c
  • rep
  • [, [[ (x,i, j, ...)
  • [<-, [[<- (x,i, j, ..., value)
  • $, $&lt;- (x, name, value)
  • summary.S3
  • Arith
    • (., ANY), (ANY, .)
  • Compare
    • (., character), (character, .)
    • (., numeric), (numeric, .)
  • as.term
    • character
    • numeric

Bonds can be created using a data.frame and spotrate can be set as one of columns.

# Declaring bonds
dc <- as.daycount('actual/360') # daycount rule
comp <- as.compounding('continuous') # compounding regime
days <- c(97, 242, 321) # days to maturity
sr <- as.spotrate(rep(0.06, length(days)), comp, dc) # discount rate

bonds <- data.frame(DaysToMaturity=days, Rate=sr, Notional=100000)
bonds
#   DaysToMaturity                              Rate Notional
# 1             97 0.06 discrete business/252 ANBIMA    1e+05
# 2            242 0.06 discrete business/252 ANBIMA    1e+05
# 3            321 0.06 discrete business/252 ANBIMA    1e+05

# Pricing bond -- discounting their notional value
within(bonds, {
  PV <- Notional*discount(Rate, DaysToMaturity)
})
#   DaysToMaturity                       Rate Notional       PV
# 1             97 0.06 continuous actual/360    1e+05 98396.33
# 2            242 0.06 continuous actual/360    1e+05 96046.92
# 3            321 0.06 continuous actual/360    1e+05 94790.59

Pricing bonds using a calendar

library(bizdays)
cal <- Calendar(holidays=holidaysANBIMA, name='ANBIMA', weekdays=c('saturday', 'sunday'))
dc <- as.daycount('business/252')
comp <- as.compounding('discrete')
dates <- as.Date(c('2014-09-07', '2015-03-07', '2015-09-07'))
sr <- as.spotrate(rep(0.06, length(dates)), comp, dc, cal)
bonds <- data.frame(RefDate=as.Date('2014-03-21'), Maturity=dates, Rate=sr, Notional=100000)
bonds
#      RefDate   Maturity                              Rate Notional
# 1 2014-03-21 2014-09-07 0.06 discrete business/252 ANBIMA    1e+05
# 2 2014-03-21 2015-03-07 0.06 discrete business/252 ANBIMA    1e+05
# 3 2014-03-21 2015-09-07 0.06 discrete business/252 ANBIMA    1e+05
within(bonds, {
  PV <- Notional*discount(Rate, from=RefDate, to=Maturity)
})
#      RefDate   Maturity                              Rate Notional       PV
# 1 2014-03-21 2014-09-07 0.06 discrete business/252 ANBIMA    1e+05 97353.43
# 2 2014-03-21 2015-03-07 0.06 discrete business/252 ANBIMA    1e+05 94558.01
# 3 2014-03-21 2015-09-07 0.06 discrete business/252 ANBIMA    1e+05 91842.86