Pricing Plain-Vanilla Bonds
Calculate the theoretical price and yield-to-maturity of a list of cashflows.
vanillaBond(cf, times, df, yields) ytm(cf, times, y0 = 0.05, tol = 1e-05, maxit = 1000L, offset = 0) duration(cf, times, yield, modified = TRUE, raw = FALSE) convexity(cf, times, yield, raw = FALSE)
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 |
yield |
numeric vector of length one (both duration and convexity assume a flat yield curve) |
y0 |
starting value |
tol |
tolerance |
maxit |
maximum number of iterations |
offset |
numeric: a ‘base’ rate over which to compute the yield to maturity. See Details and Examples. |
modified |
logical: return modified duration? (default |
raw |
logical: default |
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 (a.k.a. internal interest rate). When used with a bond, the initial
outlay (i.e. the bonds dirty price) needs be included in the vector of
cashflows. For a coupon bond, a good starting value y0 is
the coupon divided by the dirty price of the bond.
An offset can be specified either as a single number or as a
vector of zero rates. See Examples.
numeric
Enrico Schumann
Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. https://www.elsevier.com/books/numerical-methods-and-optimization-in-finance/gilli/978-0-12-815065-8
## ytm
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)
## ... with offset
cf <- c(5, 5, 5, 5, 5, 105) ## cashflows
times <- 1:6 ## maturities
y <- 0.02 + 0.01 ## risk-free 2% + risk-premium 1%
b0 <- vanillaBond(cf, times, yields = y)
cf <- c(-b0, cf); times <- c(0, times)
ytm(cf, times, offset = 0.02) ## ... only the risk-premium
cf <- c(5, 5, 5, 5, 5, 105) ## cashflows
times <- 1:6 ## maturities
y <- NS(c(6,9,10,5)/100, times) ## risk-premium 1%
b0 <- vanillaBond(cf, times, yields = y + 0.01)
cf <- c(-b0, cf); times <- c(0, times)
ytm(cf, times, offset = c(0,y)) ## ... only the risk-premium
## bonds
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)
vanillaBond(cf = M, times = alltimes, yields = 0.02)
## duration/convexity
cf <- c(5, 5, 5, 5, 5, 105) ## cashflows
times <- 1:6 ## maturities
y <- 0.0527 ## yield to maturity
d <- 0.001 ## change in yield (+10 bp)
vanillaBond(cf, times, yields = y + d) - vanillaBond(cf, times, yields = y)
duration(cf, times, yield = y, raw = TRUE) * d
duration(cf, times, yield = y, raw = TRUE) * d +
convexity(cf, times, yield = y, raw = TRUE)/2 * d^2Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.