R: Basis Curve

basis.curve {QuantBondCurves}

R Documentation

Basis Curve

Description

Function that calibrates a "discount basis rate" curve according to data of cross currency swaps. Available methods are bootstrapping or residual sum of squares (RSS) between the value of a given or inferred fixed foreign leg and the value of the local leg.

Usage

basis.curve(
  swaps,
  ex.rate = NULL,
  analysis.date = Sys.Date(),
  rates,
  rates2,
  freq = 1,
  rate.type = 1,
  daycount = "ACT/365",
  npieces = NULL,
  obj = "Price",
  Weights = NULL,
  nsimul = 1,
  piece.term = NULL,
  nodes = seq(0, 15, 0.001),
  approximation = "constant"
)

Arguments

`swaps`	Matrix containing relevant information of cross currency swaps where each row represents a swap and each column represents the next attributes: maturity, legs, coupon rate of local leg, coupon rate of foreign leg, spread of local leg, spread of variable leg, principal of local and principal of variable leg. `colnames(swaps)` must be defined as the following: `c("Mat", "Legs", "C1", "C2", "spread1", "spread2", "prin1", "prin2")`.
`ex.rate`	Exchange rate on analysis date. Format has to be local currency divided by foreign currency.
`analysis.date`	Date in which the asset is valued. By default, the current date.
`rates`	Discount rates given by the local zero coupon rate curve. The curve has to have nodes with at least, with 3 decimals.
`rates2`	Discount rates given by the foreign zero coupon rate curve. The curve has to have nodes with at least, with 3 decimals.
`freq`	Frequency of payments of a given asset in a year. For LIBOR and IBR the default frequency is four (quarterly payments). TES has a default frequency of one (annual payments).
`rate.type`	(1) for discrete compounded discount rates and (0) for continuosly compounded discount rates. By default rates are assumed to be discrete.
`daycount`	Day count convention. See also 'Details'.
`npieces`	Number of constant or linear segments for the curve to have. By default `NULL`, and bootstrapping method is used, otherwise, minimization of RSS is used.
`obj`	String related to the definition of the error in the RSS methodology. Set `"Price"` for minimization of error by price or `"Rate"` for minimization of error by rate.
`Weights`	Vector of weights used to dot product with residual squares in order to calculate residual sum of squares. By default, each residual is assigned the same weight.
`nsimul`	Number of simulations for the terms of the pieces. The more simulations, the more likely to find a better local solution. By default `1`, and terms are defined in such way each piece occupies the same length in the abscissa axis.
`piece.term`	Vector that establishes a unique term structure for optimization to take place. Each piece or segment must have a unique maturity, as numeric value in years, that signifies the end of the segment. Last segment maturity must not be introduced, it is assumed to be equivalent to the last term introduced on analysis date. Therefore, the `piece.term` vector must always have a length equal to `npieces` - 1.
`nodes`	Desired output nodes of the curve.
`approximation`	String that establish the approximation. Set `'linear'` for a linear approximation, or `'constant'` for a piecewise constant function.

Details

daycount convention accepts the following values:

30/360.
ACT/365.
ACT/360 (Default).
ACT/365L.
NL/365.
ACT/ACT-ISDA
ACT/ACT-AFB

swaps["Legs"] makes reference to the following types of legs composition of the cross currency swaps.

"FF" for fixed leg in local currency and fixed leg in foreign currency.
"FV" for fixed leg in local currency and variable leg in foreign currency.
"VF" for variable leg in local currency and fixed leg in foreign currency.
"VV" for variable leg in local currency and variable leg in foreign currency.

Value

Constant or Linear piecewise basis curve.

Author(s)

Camilo Díaz

Examples

# Inputs for calibration of spot curve
yield.curve  <- c(0.015,0.0175, 0.0225, 0.0275, 0.0325, 0.0375,0.04,0.0425,0.045,0.0475,0.05)
names(yield.curve) <- c(0.5,1,2,3,4,5,6,7,8,9,10)
nodes <- seq(0,10,0.001)
# Calibration of local spot curve
rates <- curve.calibration (yield.curve = yield.curve, market.assets = NULL,
                            analysis.date = "2019-01-03" , asset.type = "IBRSwaps",
                            freq = 4, rate.type = 0, fwd = 0, npieces = NULL,
                            obj = "Price", nodes = nodes, approximation = "linear")
# Input for Basis Curve
ex.rate <- 4814
swaps <- rbind(c("2024-03-01", "FF", 0.07 , 0.0325, NA   , NA    , 2000 * ex.rate, 2000),
               c("2025-03-01", "VV", NA   , NA    , 0.015, 0.0175, 2000 * ex.rate, 2000),
               c("2026-03-01", "FF", 0.075, 0.03  , NA   ,  NA   , 5000000, 5000000 / ex.rate),
               c("2027-03-01", "VV", NA   , NA    , 0.01 , 0.015 , 5000000, 5000000 / ex.rate),
               c("2028-03-01", "FF", 0.08 ,0.035  , NA   , NA    , 3000000, 3000000 / ex.rate),
               c("2029-03-01", "VV", NA   , NA    , 0.01 , 0.0125, 3000000, 3000000 / ex.rate))
colnames(swaps) <- c("Mat"  ,"Legs", "C1" , "C2", "spread1", "spread2", "prin1", "prin2")
# Function
basis.curve(swaps = swaps, ex.rate = 4814, analysis.date = "2023-03-01",
            rates = rates, rates2 = rates / 4, freq = c(2,2,2,2,1,1),
            rate.type = 1, npieces = 4, obj = "Price", Weights = NULL,
            nsimul = 1, nodes = nodes, approximation = "linear")

[Package QuantBondCurves version 0.3.0 Index]