This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

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 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.

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

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 (BMA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see basis.

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.

Note

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

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 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 DatesBond A RatesBond B DatesBond B RatesBond C DatesBond 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

This function adheres to SIA Fixed Income Securities Formulas for Price, Yield, and Accrued Interest. 3rd Edition. Vol. 1, pp. 120–123, on zero-coupon instruments pricing.

Introduced before R2006a