bondConvexity

Syntax

bondConvexity(start, maturity, issuePrice, coupon, frequency, dayCountConvention, bondType, settlement, price, priceType, [benchmark='Excel'])

Details

bondConvexity returns the bond convexity of a bond with a face value of 100. Bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates.

Parameters

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
  • "ActualActualISMA" (default): actual/actual (ISMA rule)
  • "Actual360": actual/360
  • "Actual365": actual/365
  • "Thirty360EU": European 30/360
  • "ActualActualISDA" (default): actual/actual (ISDA rule)
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 indicating the bond's yield to maturity.

priceType is a STRING scalar or vector used to specify the type of the bond price (price). Currently, only "YTM" (Yield to Maturity) is supported.

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

Returns

A scalar or vector of type DOUBLE.

Examples

bondConvexity(start=2023.01.01, maturity=2030.12.31, issuePrice=100, coupon=0.05, frequency=1, dayCountConvention="ActualActualISMA", bondType="FixedRate", settlement=2023.04.01, price=0.03, priceType="YTM")
// output: 51.864347713454684