Fixed-Income Toolbox™

stepcpnprice - Price bond with stepped coupons

Syntax

[Price, AccruedInterest] = stepcpnprice(Yield, Settle, Maturity, 
ConvDates, CouponRates, Period, Basis, EndMonthRule, Face)

Arguments

`Yield`	Scalar or vector containing yield to maturity of instruments.
`Settle`	Settlement date. A scalar or vector of serial date numbers. `Settle` must be earlier than or equal to `Maturity`.
`Maturity`	Maturity date. A scalar or vector of serial date numbers.
`ConvDates`	Matrix of serial date numbers representing conversion dates after `Settle`. Size = number of instruments by maximum number of conversions. Fill unspecified entries with `NaN`.
`CouponRates`	Matrix indicating the coupon rates for each bond in decimal form. Size = number of instruments by maximum number of conversions + 1. First column of this matrix contains rates applicable between `Settle` and the first conversion date (date in the first column of `ConvDates`). Fill unspecified entries with `NaN`. See Note below.
`Period`	(Optional) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2, 3, 4, 6, and 12. Default = 2.
`Basis`	(Optional) Day-count basis of the instrument. A vector of integers. 0 = actual/actual (default) 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)
`EndMonthRule`	(Optional) 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's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.
`Face`	(Optional) Face value of each bond in the portfolio. Default = 100.

All arguments must be scalars or number of bonds (NUMBONDS)-by-1 vectors, except for ConvDates and CouponRates.

Note ConvDates has the same number of rows as CouponRate to reflect the same number of bonds. However, ConvDates has one less column than CouponRate. This situation is illustrated by

Settle---------ConvDate1-----------ConvDate2------------Maturity

        Rate1               Rate2                 Rate3

Description

[Price, AccruedInterest] = stepcpnprice(Yield, Settle, Maturity, ConvDates, CouponRates, Period, Basis, EndMonthRule, Face) computes the price of bonds with stepped coupons given the yield to maturity. The function supports any number of conversion dates.

Price is a NUMBONDS-by-1 vector of clean prices.

AccruedInterest is a NUMBONDS-by-1 vector of accrued interest payable at settlement dates.

Note For bonds with fixed coupons, use bndprice. If you use a fixed-coupon bond with stepcpnprice, you will receive the error: incorrect number of inputs.

Examples

Compute the price and accrued interest due on a portfolio of stepped-coupon bonds having a yield of 7.221%, given three conversion scenarios:

Bond A has two conversions, the first one falling on the settle date and immediately expiring.
Bond B has three conversions, with conversion dates exactly on the coupon dates.
Bond C has three conversions, with one or more conversion dates not on coupon dates. This case illustrates that only cash flows for full periods after conversion dates are affected, as illustrated below.

The following table illustrates the interest rate characteristics of this bond portfolio.

Bond A Dates	Bond A Rates	Bond B Dates	Bond B Rates	Bond C Dates	Bond C Rates
Settle (02-Aug-92)	7.5%	Settle (02-Aug-92)	7.5%	Settle (02-Aug-92)	7.5%
First Conversion (02-Aug-92)	8.875%	First Conversion (15-Jun-97)	8.875%	First Conversion (14-Jun-97)	8.875%
Second Conversion (15-Jun-03)	9.25%	Second Conversion (15-Jun-01)	9.25%	Second Conversion (14-Jun-01)	9.25%
Maturity (15-Jun-10)	`NaN`	Third Conversion (15-Jun-05)	10.0%	Third Conversion (14-Jun-05)	10.0%
		Maturity (15-Jun-10)	`NaN`	Maturity (15-Jun-10)	`NaN`

Yield = 0.07221;
Settle   = datenum('02-Aug-1992');
ConvDates = [datenum('02-Aug-1992'), datenum('15-Jun-2003'),... 
             nan;
            datenum('15-Jun-1997'), datenum('15-Jun-2001'),... 
            datenum('15-Jun-2005');
            datenum('14-Jun-1997'), datenum('14-Jun-2001'),... 
            datenum('14-Jun-2005')];
Maturity = datenum('15-Jun-2010');

CouponRates = [0.075 0.08875 0.0925 nan;
               0.075 0.08875 0.0925 0.1;
               0.075 0.08875 0.0925 0.1];
Basis = 1;
Period = 2;
EndMonthRule = 1;
Face = 100;

[Price, AccruedInterest] = ...
stepcpnprice(Yield, Settle, Maturity, ConvDates, CouponRates, ... 
Period, Basis, EndMonthRule, Face)

Price =

  117.3824
  113.4339
  113.4339

AccruedInterest =

    1.1587
    0.9792
    0.9792

References