bndconvy

Bond convexity given yield

Syntax

[YearConvexity, PerConvexity] = bndconvy(Yield, CouponRate,
Settle, Maturity)
[YearConvexity, PerConvexity] = bndconvy(Yield,
CouponRate, Settle, Maturity, Period, Basis, EndMonthRule,
IssueDate, FirstCouponDate, LastCouponDate, StartDate,
Face)
[YearConvexity, PerConvexity] = bndconvy(Yield,
CouponRate, Settle, Maturity,
'ParameterName', 'ParameterValue ...)

Description

[YearConvexity, PerConvexity] = bndconvy(Yield, CouponRate,
Settle, Maturity)
computes the convexity of NUMBONDS fixed income securities given the yield to maturity for each bond.

[YearConvexity, PerConvexity] = bndconvy(Yield,
CouponRate, Settle, Maturity, Period, Basis, EndMonthRule,
IssueDate, FirstCouponDate, LastCouponDate, StartDate,
Face)
computes the convexity of NUMBONDS fixed income securities given the yield to maturity for each bond using optional arguments.

[YearConvexity, PerConvexity] = bndconvy(Yield,
CouponRate, Settle, Maturity,
'ParameterName', 'ParameterValue ...)
computes the convexity of NUMBONDS fixed income securities given the yield to maturity for each bond and accepts optional inputs as one or more comma-separated parameter/value pairs. 'ParameterName' is the name of the parameter inside single quotes. ParameterValue is the value corresponding to 'ParameterName'. Specify parameter/value pairs in any order. Names are case-insensitive.

Input Arguments

Yield

Yield to maturity on a semiannual basis.

CouponRate

Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.

Settle

Settlement date. A vector of serial date numbers or date strings. Settle must be earlier than Maturity.

Maturity

Maturity date. A vector of serial date numbers or date strings.

Ordered Input or Parameter–Value Pairs

Enter the following inputs using an ordered syntax or as parameter/value pairs. You cannot mix ordered syntax with parameter/value pairs.

Period

Coupons per year of the bond. A vector of integers. Values are 0, 1, 2, 3, 4, 6, and 12.

Default: 2

Basis

Day-count basis of the instrument. A vector of integers.

  • 0 = actual/actual

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (PSA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ISMA)

  • 9 = actual/360 (ISMA)

  • 10 = actual/365 (ISMA)

  • 11 = 30/360E (ISMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see basis.

Default: 0

EndMonthRule

End-of-month rule. A vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month. 1 = set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Default: 1

IssueDate

Issue date for a bond.

FirstCouponDate

Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

Default: If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

LastCouponDate

Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date.

Default: If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

StartDate

Date when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date. If you do not specify StartDate, the effective start date is the Settle date.

Face

Face or par value.

Default: 100

Parameter–Value Pairs

Enter the following inputs only as parameter/value pairs.

CompoundingFrequency

Compounding frequency for yield calculation. By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ISMA bases (8-12) use an annual compounding convention.

DiscountBasis

Basis used to compute the discount factors for computing the yield. The default behavior is for SIA bases to use the actual/actual day count to compute discount factors. If you use ISMA day counts and BUS/252, the specified bases are used.

Output Arguments

YearConvexity

NUMBONDS-by-1 vector for the yearly (annualized) convexity.

PerConvexity

NUMBONDS-by-1 vector for the periodic convexity reported on a semiannual bond basis (in accordance with SIA convention).

Definitions

bndconvy determines the convexity for a bond whether the first or last coupon periods in the coupon structure are short or long (that is, whether the coupon structure is synchronized to maturity). This function also determines the convexity of a zero coupon bond.

All specified arguments must be number of bonds (NUMBONDS)-by-1 or 1-by-NUMBONDS conforming vectors or scalar arguments. Use an empty matrix ([]) as a placeholder for an optional argument. Fill in unspecified entries input vectors with NaNs. Dates can be serial date numbers or date strings.

Examples

expand all

Find Bond Convexity Given Yield

This example shows how to compute the convexity of a bond at three different yield values.

Yield = [0.04; 0.055; 0.06];
CouponRate = 0.055;
Settle = '02-Aug-1999';
Maturity = '15-Jun-2004';
Period = 2;
Basis = 0;

[YearConvexity, PerConvexity]=bndconvy(Yield, CouponRate,...
Settle, Maturity, Period, Basis)
YearConvexity =

   21.4825
   21.0358
   20.8885


PerConvexity =

   85.9298
   84.1434
   83.5541

References

Krgin, Dragomir, Handbook of Global Fixed Income Calculations, John Wiley & Sons, 2002.

Mayle, Jan, "Standard Securities Calculations Methods: Fixed Income Securities Formulas for Analytic Measures", SIA, Vol 2, Jan 1994.

Stigum, Marcia, and Franklin Robinson, Money Market and Bond Calculations, McGraw-Hill, 1996.

See Also

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