bonds: Pricing Plain-Vanilla Bonds

In NMOF: Numerical Methods and Optimization in Finance

Description

Calculate the theoretical price and yield-to-maturity of a list of cashflows.

Usage

vanillaBond(cf, times, df, yields)
ytm(cf, times, y0 = 0.05, tol = 1e-05, maxit = 1000L)        

Arguments

cf	Cashflows; a numeric vector or a matrix. If a matrix, cashflows should be arranged in rows; times-to-payment correspond to columns.
times	times-to-payment; a numeric vector.
df	discount factors; a numeric vector.
yields	optional (instead of discount factors); zero yields to compute discount factor; if of length one, a flat zero curve is assumed
y0	starting value
tol	tolerance
maxit	maximum number of iterations

Details

vanillaBond computes the present value of a vector of cashflows; it may thus be used to evaluate not just bonds but any instrument that can be reduced to a deterministic set of cashflows.

ytm uses Newton's method to compute the yield-to-maturity of a bond (or internal interest rate). When used with a bond, the initial outlay (ie, the bonds dirty price) needs be included in the vector of cashflows.

Value

Numeric.

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2011) Numerical Methods and Optimization in Finance. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626

See Also

NS, codeNSS

Examples

cf <- c(5, 5, 5, 5, 5, 105)   ## cashflows
times <- 1:6                  ## maturities
y <- 0.0127                   ## the "true" yield
b0 <- vanillaBond(cf, times, yields = y)
cf <- c(-b0, cf); times <- c(0, times)
ytm(cf, times)

##
cf <- c(5, 5, 5, 5, 5, 105)   ## cashflows
times <- 1:6                  ## maturities
df <- 1/(1+y)^times           ## discount factors
all.equal(vanillaBond(cf, times, df),
          vanillaBond(cf, times, yields = y))

## using Nelson--Siegel
vanillaBond(cf, times, yields = NS(c(0.03,0,0,1), times))


## several bonds
##   cashflows are numeric vectors in a list 'cf',
##   times-to-payment are are numeric vectors in a
##   list 'times'

times <- list(1:3,
              1:4,
              0.5 + 0:5)
cf <- list(c(6, 6,          106),
           c(4, 4, 4,       104),
           c(2, 2, 2, 2, 2, 102))

alltimes <- sort(unique(unlist(times)))
M <- array(0, dim = c(length(cf), length(alltimes)))
for (i in seq_along(times))
    M[i, match(times[[i]], alltimes)] <- cf[[i]]
rownames(M) <- paste("bond.", 1:3, sep = "")
colnames(M) <- format(alltimes, nsmall = 1)
M

vanillaBond(cf = M, times = alltimes, yields = 0.02)

NMOF documentation built on May 2, 2019, 6:39 p.m.