fwd2spot {QuantBondCurves}

Forward curve conversion

Description

Uses a recursive method to calculate the implicit spot rates of a given forward curve. Calculations and formulas based on the definition of forward rates where \exp{-rT} = \exp{-\int{f(t)dt}}.

Usage

fwd2spot(dates, fwd, approximation = "constant")

Arguments

dates

Term structure of rates.

fwd

Numeric vector of forward rates to be converted.

approximation

String that establish the approximation. Set 'linear' for a piecewise linear approximation, or 'constant' for a piecewise constant curve.

Details

Requires continuous rates. Recommended that the input forward curve starts with maturity 0, if not, function will approximate zero node as equal to node 1 (first term structure). Output forward curve slightly differs from empirical curve as it calculates an implicit forward curve.

Value

Implicit spot curve based on the input forward rates and input term structure.

Examples

# Inputs for calibration of forward 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(0,10,0.5)
# Calibration
fwd <- curve.calibration (yield.curve = yield.curve, market.assets = NULL,
                          analysis.date = "2019-01-03", asset.type = "IBRSwaps",
                          freq = 4, rate.type = 0, daycount = "ACT/365",  fwd = 1,
                          npieces = NULL, nodes = nodes, approximation = "constant")
# Forward to Spot
dates <- names(fwd)
fwd2spot(dates, fwd, approximation = "constant")