bndspread - Static spread over spot curve

Syntax

Spread = bndspread(SpotInfo, Price, Coupon, Settle, Maturity) Spread = bndspread(SpotInfo, Price, Coupon, Settle, Maturity Period, Basis, EndMonthRule, IssueDate, FirstCouponDate LastCouponDate, StartDate, Face) Spread = bndspread(SpotInfo, Price, Coupon, Settle, Maturity, 'ParameterName', 'ParameterValue ...)

Description

Spread = bndspread(SpotInfo, Price, Coupon, Settle, Maturity) computes the static spread (Z-spread) to benchmark in basis points.

Spread = bndspread(SpotInfo, Price, Coupon, Settle, MaturityPeriod, Basis, EndMonthRule, IssueDate, FirstCouponDateLastCouponDate, StartDate, Face) computes the static spread (Z-spread) to benchmark in basis points including optional inputs.

Spread = bndspread(SpotInfo, Price, Coupon, 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.

Input Arguments

`SpotInfo`	Two-column matrix: `[SpotDates ZeroRates]`. Zero rates correspond to maturities on the spot dates, continuously compounded. Choose evenly spaced rates close together to obtain the best results. For example, using the 3-month deposit rates: SpotInfo = ... [datenum('2-Jan-2004') , 0.03840; datenum('2-Jan-2005') , 0.04512; datenum('2-Jan-2006') , 0.05086];
`Price`	Price for every $100 notional amount of bonds whose spreads are computed. This is the clean price of the bond (current price without accrued interest).
`Coupon`	Annual coupon rate of bonds whose spreads are computed.
`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

Spread

Static spread to benchmark, in basis points.

Examples

Compute a Federal National Mortgage Association (FNMA) 4 3/8 spread over a Treasury spot curve:

RefMaturity = [datenum('02/27/2003');    
               datenum('05/29/2003');
               datenum('10/31/2004');
               datenum('11/15/2007');
               datenum('11/15/2012');
               datenum('02/15/2031')];

RefCpn = [0;
          0;
          2.125;
          3;
          4;
          5.375] / 100;

RefPrices =  [99.6964;
              99.3572;
             100.3662;
              99.4511;
              99.4299;
             106.5756];
         
RefBonds = [RefPrices, RefMaturity, RefCpn];
Settle   = datenum('26-Nov-2002');
[ZeroRates, CurveDates] = zbtprice(RefBonds(:, 2:end), ... 
RefPrices, Settle)

% FNMA 4 3/8 maturing 10/06 at 4.30 pm Tuesday
Price    = 105.484;
Coupon   = 0.04375;
Maturity = datenum('15-Oct-2006');

% All optional inputs are supposed to be accounted by default,
% except the accrued interest under 30/360 (SIA), so:
Period = 2;
Basis  = 1;
SpotInfo = [CurveDates, ZeroRates];

% Compute static spread over treasury curve, taking into account
% the shape of curve as derived by bootstrapping method embedded 
% within bndspread.

SpreadInBP = bndspread(SpotInfo, Price, Coupon, Settle, ...  
Maturity, Period, Basis)

This returns:

ZeroRates =

    0.0121
    0.0127
    0.0194
    0.0317
    0.0423
    0.0550

CurveDates =

      731639
      731730
      732251
      733361
      735188
      741854

SpreadInBP =

   18.7582

Plot the results:

plot(CurveDates, ZeroRates*100, 'b', CurveDates, ... 
ZeroRates*100+SpreadInBP/100, 'r--')
legend({'Treasury'; 'FNMA 4 3/8'})
xlabel('Curve Dates')
ylabel('Spot Rate [%]')
grid;

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.

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