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Price of a level coupon bond from its yield

Source: R/bond_price.R
bond_price.Rd

Computes the dirty price of a level coupon bond at time 0 from its yield, using compact actuarial notation.

Usage

bond_price(
  face,
  c,
  n,
  k = 1L,
  y_effective_per_period = NULL,
  y = NULL,
  y_type = "effective",
  y_m = 1L,
  R = NULL,
  tol = 1e-10,
  check = TRUE
)

Arguments

face

Numeric scalar. Face value of the bond.

c

Numeric scalar. Annual coupon rate as a proportion.

n

Numeric scalar. Time to maturity in years.

k

Positive integer. Number of coupon payments per year.

y_effective_per_period

Optional numeric scalar. Effective yield per coupon period. If supplied, it is used directly.

y

Optional numeric scalar. Annual yield rate value.

y_type

Character string indicating the annual yield type: "effective", "nominal_interest", "nominal_discount", or "force".

y_m

Positive integer. Conversion frequency for nominal annual yields.

R

Numeric scalar. Redemption value at maturity. If NULL, defaults to face.

tol

Finite positive numeric scalar. Tolerance used when checking alignment of maturity with coupon periods.

check

Logical scalar. If TRUE, performs basic input validation.

Value

Numeric scalar: dirty price of the bond at time 0.

Details

Assumptions:

  • Coupons are paid in arrears at regular intervals.

  • n * k must be an integer.

  • Stub periods are not supported.

  • No accrued interest is considered; the price is evaluated at a coupon date.

The yield may be supplied in either of two ways:

  • directly as an effective yield per coupon period through y_effective_per_period, or

  • as an annual rate specification through y, y_type, and y_m.

Annual yield specifications are valued using their original log accumulation rate, avoiding loss of precision or range in intermediate annual equivalents.

This function follows the compact bond notation used in tidyactuarial: face is the face value, c is the annual coupon rate, n is the time to maturity, k is the coupon frequency, y is the annual yield input, and R is the redemption value.

Let \(j\) be the effective yield per coupon period, \(k\) the number of coupon payments per year, and let \(N = nk\) be the total number of coupon periods. With coupon per period \(C = face \cdot c/k\) and discount factor \(v = 1/(1+j)\), the price is: $$P = \sum_{r=1}^{N} C_r v^r,$$ where the sum runs over all coupon and redemption cash flows indexed by coupon period \(r\).

See also

bond_ytm, bond_cash_flows, bond_duration, bond_convexity, bond_book_value, bond_callable_price

Other bonds: accrued_interest(), bond_book_value(), bond_callable_price(), bond_convexity(), bond_duration(), bond_ytm(), portfolio_convexity(), portfolio_duration()

Examples

# 5-year annual coupon bond, yield given as annual effective
bond_price(
  face = 100,
  c = 0.08,
  n = 5,
  k = 1,
  y = 0.06,
  y_type = "effective"
)
#> [1] 108.4247

# 10-year semiannual bond, yield given directly per coupon period
bond_price(
  face = 1000,
  c = 0.05,
  n = 10,
  k = 2,
  y_effective_per_period = 0.03
)
#> [1] 925.6126

# Semiannual coupons, nominal annual yield convertible quarterly
bond_price(
  face = 100,
  c = 0.08,
  n = 5,
  k = 2,
  y = 0.06,
  y_type = "nominal_interest",
  y_m = 4
)
#> [1] 108.3287