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)

[YearConvexity, PerConvexity] = bndconvy(Yield, CouponRate, Settle, Maturity, 'ParameterName','ParameterValue ...) 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.

Inputs

`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 or equal to `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 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`	Irregular or normal first coupon date.
`LastCouponDate`	Irregular or normal last coupon date.
`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.

Outputs

`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

Find 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)

This returns:

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.

How To

Yield Conventions

bndconvp

bnddurp

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