QuantBondCurves (version 0.3.2)

curve.calibration: Curve calibration

Description

Function that calibrates and returns a Zero Coupon curve based on the coupon rates and IRR's of the assets. Uses the bootstrap method to find, recursively, the corresponding Zero Coupon rates given by the market data. This rates are then optimized by the minimization of the MAE between bond values given by the constructed rates and bond market value. Alternatively, uses minimization of residual sum of squares (RSS), allowing user to optimize or define an specific term structure of the segments.

Usage

curve.calibration(
  yield.curve,
  market.assets = NULL,
  noSpots = NULL,
  analysis.date = Sys.Date(),
  asset.type = "IBRSwaps",
  freq = 4,
  rate.type = 0,
  daycount = NULL,
  fwd = 0,
  npieces = NULL,
  obj = "Price",
  Weights = NULL,
  nsimul = 1,
  piece.term = NULL,
  nodes = seq(0, 10, 0.001),
  approximation = "linear"
)

Value

Zero Coupon curve for a specific date based on historical spot rates and bond structures.

Arguments

yield.curve

Internal rates of return of the market assets. Series of rates with different maturities that adjust to the time structure of the curve to calibrate and construct. names(yield.curve) needs to include the numeric maturities in years of each rate, unless the input market.assets includes the maturities as dates.

market.assets

Matrix containing the market assets. The first column contains the coupon rates of the assets and the second column represents their corresponding maturities as a date. This input is only required if IRR's of assets differ from coupon rate.

noSpots

Number of spot interest rates introduced in the yield.curve input. Function assumes spots are the first entries on the yield.curve vector.

analysis.date

Date for which the curve is going to be calibrated and, thus, constructed.

asset.type

String that determines the asset type to value. See also 'Details'.

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 annual compounded discount rates and (0) for continuosly compounded discount rates. By default, rates are assumed to be the former.

daycount

Day count convention. See also 'Details'.

fwd

Numeric value that determines if the desired output curve is a forward or a spot curve. Set 0 for spot curve (default), 1 otherwise.

npieces

Number of constant or linear segments for the curve to incorporate. 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 piecewise linear approximation, or 'constant' for a piecewise constant curve.

Author

Andres Galeano & Camilo Díaz

Details

asset.type makes reference to the following type of assets:

• "TES" for Colombian Treasury Bonds (default).

• "IBRSwaps" for swaps indexed to IBR rate.

• "LIBORSwaps" for Interest Rate Swaps (IRS) indexed to 3M LIBOR.

• "FixedIncome" for assets that are indexed to a fixed income with different frequency of payments.

If npieces = NULL uses a recursive iteration process based in bootstrapping where the curve is constructed through a minimization of the MAE between the dirty price of historical market assets and an approximation of the theoretical price of assets of same maturity. Uses the "L-BFGS-B" optimization method to minimize the expected MAE. Otherwise, curve is constructed through minimization of RSS where the error can be defined via price or rate.

Examples

# Create input
yield.curve <- c(0.103,0.1034,0.1092, 0.1161, 0.1233, 0.1280, 0.1310, 0.1320, 0.1325, 0.1320)
names(yield.curve) <- c(0,0.08,0.25,0.5,1,2,3,5,7,10)
nodes <- seq(0,10,0.001)

market.assets <- matrix(NA,nrow = 10,ncol = 2)
market.assets[1,1] <- 0.1030 ; market.assets[2,1]  <- 0.1044
market.assets[3,1] <- 0.1083 ; market.assets[4,1]  <- 0.1010
market.assets[5,1] <- 0.1120 ; market.assets[6,1]  <- 0.1130
market.assets[7,1] <- 0.1150 ; market.assets[8,1]  <- 0.1160
market.assets[9,1] <- 0.1150 ; market.assets[10,1] <- 0.13
market.assets[1,2] <- "2019-01-03" ; market.assets[2,2]  <- "2019-02-03"
market.assets[3,2] <- "2019-04-03" ; market.assets[4,2]  <- "2019-07-03"
market.assets[5,2] <- "2020-01-03" ; market.assets[6,2]  <- "2021-01-03"
market.assets[7,2] <- "2022-01-03" ; market.assets[8,2]  <- "2024-07-03"
market.assets[9,2] <- "2026-01-03" ; market.assets[10,2] <- "2029-01-03"

# Function
curve.calibration (yield.curve = yield.curve, market.assets = market.assets,
                  analysis.date = "2019-01-03" , asset.type = "IBRSwaps",
                  freq = 4, daycount = "ACT/365", fwd = 0, nodes = nodes,
                  approximation = "linear")