spot2forward {QuantBondCurves}

Spot curve conversion

Description

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

Usage

spot2forward(dates, spot, approximation = "constant")

Arguments

dates

Term structure of rates.

spot

Vector of spot 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 spot curve starts with maturity 0, if not, input function will approximate zero node as equal to node 1 (first term structure). The time partition and available data affects calculation and precision of resulting forward curve. Output forward curve slightly differs from empirical curve as it calculates an implied instantaneous forward curve.

Value

Instantaneous forward curve based on the input spot and the input term structure.

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
spot <- 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")
# Spot to Forward
dates <- names(spot)
spot2forward(dates, spot, approximation = "linear")