bondYield

Syntax

bondYield(start, maturity, issuePrice, coupon, frequency, dayCountConvention, bondType, settlement, price, priceType, [method='newton'], [maxIter=100], [benchmark='Excel'])

Arguments

Note: Scalar inputs will be automatically expanded to match the length of other vector inputs. All vector inputs must be of equal length.

start is a scalar or vector of DATE type, indicating the bond’s value date.

maturity is a DATE scalar or vector indicating the maturity date.

issuePrice is a numeric scalar or vector of the same length as start indicating the bond’s issue price. For discount bonds, the actual issue price must be specified (typically less than 100); for other bonds, it is usually 100.

coupon is a numeric scalar or vector indicating the annual coupon rate. For example, 0.03 indicates a 3% annual coupon.

frequency is an INT scalar/vector indicating the number of payments, or a STRING scalar/vector indicating payment frequency. It can be:
  • 0/"Once": Bullet payment at maturity.
  • 1/"Annual": Annual payments.
  • 2/"Semiannual": Semi-annual payments.
  • 4/"Quarterly": Quarterly payments.
  • 12/"Monthly": Monthly payments.
dayCountConvention is a STRING scalar or vector indicating the day count convention to use. It can be:
  • "Thirty360US": US (NASD) 30/360
  • "ActualActual" (default): actual/actual
  • "Actual360": actual/360
  • "Actual365": actual/365
  • "Thirty360EU": European 30/360
bondType is a STRING scalar or vector indicating the bond type. It can be:
  • "FixedRate": Fixed-rate bond, where interest is paid periodically based on the coupon rate.
  • "Discount": Discount bond, where no interest is paid, and the bond is issued at a discount. FV at maturity = face value.
  • "ZeroCoupon": Zero-coupon bond, where interest and face value are paid at maturity. FV at maturity = face value + interest.

settlement is a DATE scalar or vector indicating the settlement date.

price is a numeric scalar or vector whose meaning depends on the value of priceType:
  • When priceType is "CleanPrice", price indicates the bond's clean price.
  • When priceType is "DirtyPrice", price indicates the bond's dirty price.
priceType is a STRING scalar or vector used to specify the type of the bond price (price). It can be:
  • "CleanPrice": Clean price.
  • "DirtyPrice": Dirty price.
method (optional) is a STRING scalar or vector indicating the optimization algorithm used to solve the bond yield. It can be:
  • "newton" (default): Newton algorithm.
  • "brent": Brent algorithm.
  • "nm": Nelder-Mead simplex algorithm.
  • "bfgs": BFGS algorithm.
  • "lbfgs": LBFGS algorithm.

maxIter (optional) is a positive integer or a vector of positive integers indicating the maximum number of iterations. The default value is 100.

benchmark (optional) is a STRING scalar indicating the reference algorithm. Currently, only "Excel" (the algorithm used in Excel) is supported.

Details

Calculate the bond yield for each 100 face value of a bond based on its clean price or dirty price.

Return value: A DOUBLE scalar or vector.

Note:

  • If there is one coupon period or less until redemption, YIELD is calculated as follows:

    where:
      • A = number of days from the beginning of the coupon period to the settlement date (accrued days).
      • DSR = number of days from the settlement date to the redemption date.
      • E = number of days in the coupon period.
  • If there is more than one coupon period until redemption, bond yield is calculated through a hundred iterations. The resolution uses the Newton method. The yield is changed until the estimated price given the yield is close to price.

  • An annual coupon rate is used by default.

Examples

bondYield(start=2023.01.01, maturity=2030.12.31, issuePrice=100, coupon=0.05, frequency=1, dayCountConvention="ActualActual", bondType="FixedRate", settlement=2023.04.01, price=100.2143, priceType="CleanPrice", method = ['newton', 'nm', 'brentq', 'bfgs','lbfgs'])

// output: [0.049624,0.049624,0.049624,0.049624,0.049629]