bondYield

bondYield(settlement, maturity, coupon, price, redemption, frequency, [basis=1], [method='newton'], [maxIter])

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

settlement is a scalar or vector of DATE type, indicating the marketable security's settlement date. The settlement date is the date after the issue date when the security is traded to the buyer.

maturity is a scalar or vector of DATE type of the same length as settlement, indicating the marketable security's maturity date. The maturity date is the date when the security expires.

coupon is a numeric scalar or vector indicating the annual coupon rate of the marketable security.

price is a numeric scalar or vector of the same length as settlement indicating the bond price per 100 face value.

redemption is a numeric scalar or vector indicating the redemption value per 100 face value.

frequency (optional) is an integer or a vector of integers indicating the number of coupon payments per year. It can be:

• 1: Annual payments
• 2: Semi-annual payments
• 4: Quarterly payments
• 12: Monthly payments

basis(optional) is an integer or a vector of integers indicating the day count basis to use. It can be:

• 0: US (NASD) 30/360
• 1 (default): actual/actual
• 2: actual/360
• 3: actual/365
• 4: European 30/360

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.

Calculate the bond yield for each 100 face value of a bond based on its 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.

Calculate the yield for a bond issued on January 15, 2008, with a maturity date of November 15, 2016, an annual coupon rate of 5.75%, a redemption price of 100, semi-annual interest payments, and a US (NASD) 30/360 day count basis, using the optimization algorithms 'newton', 'nm', 'brentq', 'bfgs', and 'lbfgs'.

settlement = 2008.02.15
maturity = 2016.11.15
coupon = 0.0575
price = 95.04287
redemption = 100
frequency = 2
basis = 0
method = ['newton', 'nm', 'brentq', 'bfgs','lbfgs']
bondYield(settlement, maturity, coupon, price, redemption, frequency, basis, method)
// Output:[0.065000006880755,0.064999847412109,0.065000006880759,0.064999999976412,0.065000004967984]