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stepcpncfamounts

Cash flow amounts and times for bonds and stepped coupons

Description

example

[CFlows,CDates,CTimes] = stepcpncfamounts(Settle,Maturity,ConvDates,CouponRates) returns matrices of cash flow amounts, cash flow dates, and time factors for a portfolio of NUMBONDS stepped-coupon bonds.

example

[CFlows,CDates,CTimes] = stepcpncfamounts(___,Period,Basis,EndMonthRule,Face) adds additional optional arguments.

Examples

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This example generates stepped cash flows for three different bonds, all paying interest semiannually. The life span of the bonds is about 18–19 years each:

  • Bond A has two conversions, but the first one occurs on the settlement date and immediately expires.

  • Bond B has three conversions, with conversion dates exactly on the coupon dates.

  • Bond C has three conversions, with some conversion dates not on the coupon dates. It has the longest maturity. This case illustrates that only cash flows for full periods after conversion dates are affected, as illustrated here:

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

Define the bond specifications.

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'); 
            datenum('15-Jun-2010'); 
            datenum('15-Jun-2011')];

CouponRates = [0.075 0.08875 0.0925 nan;
               0.075 0.08875 0.0925 0.1;
               0.025 0.05    0.0750 0.1];
Basis = 1;
Period = 2;
EndMonthRule = 1;
Face = 100;

Use stepcpncfamounts to compute cash flows and timings.

[CFlows, CDates, CTimes] = stepcpncfamounts(Settle, Maturity, ConvDates, CouponRates)
CFlows = 3×39

   -1.1639    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250  104.6250       NaN       NaN
   -0.9836    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.4375    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    4.6250    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000  105.0000       NaN       NaN
   -0.3279    1.2500    1.2500    1.2500    1.2500    1.2500    1.2500    1.2500    1.2500    1.2500    2.5000    2.5000    2.5000    2.5000    2.5000    2.5000    2.5000    2.5000    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    3.7500    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000    5.0000  105.0000

CDates = 3×39

      727778      727913      728095      728278      728460      728643      728825      729008      729191      729374      729556      729739      729921      730104      730286      730469      730652      730835      731017      731200      731382      731565      731747      731930      732113      732296      732478      732661      732843      733026      733208      733391      733574      733757      733939      734122      734304         NaN         NaN
      727778      727913      728095      728278      728460      728643      728825      729008      729191      729374      729556      729739      729921      730104      730286      730469      730652      730835      731017      731200      731382      731565      731747      731930      732113      732296      732478      732661      732843      733026      733208      733391      733574      733757      733939      734122      734304         NaN         NaN
      727778      727913      728095      728278      728460      728643      728825      729008      729191      729374      729556      729739      729921      730104      730286      730469      730652      730835      731017      731200      731382      731565      731747      731930      732113      732296      732478      732661      732843      733026      733208      733391      733574      733757      733939      734122      734304      734487      734669

CTimes = 3×39

         0    0.7377    1.7377    2.7377    3.7377    4.7377    5.7377    6.7377    7.7377    8.7377    9.7377   10.7377   11.7377   12.7377   13.7377   14.7377   15.7377   16.7377   17.7377   18.7377   19.7377   20.7377   21.7377   22.7377   23.7377   24.7377   25.7377   26.7377   27.7377   28.7377   29.7377   30.7377   31.7377   32.7377   33.7377   34.7377   35.7377       NaN       NaN
         0    0.7377    1.7377    2.7377    3.7377    4.7377    5.7377    6.7377    7.7377    8.7377    9.7377   10.7377   11.7377   12.7377   13.7377   14.7377   15.7377   16.7377   17.7377   18.7377   19.7377   20.7377   21.7377   22.7377   23.7377   24.7377   25.7377   26.7377   27.7377   28.7377   29.7377   30.7377   31.7377   32.7377   33.7377   34.7377   35.7377       NaN       NaN
         0    0.7377    1.7377    2.7377    3.7377    4.7377    5.7377    6.7377    7.7377    8.7377    9.7377   10.7377   11.7377   12.7377   13.7377   14.7377   15.7377   16.7377   17.7377   18.7377   19.7377   20.7377   21.7377   22.7377   23.7377   24.7377   25.7377   26.7377   27.7377   28.7377   29.7377   30.7377   31.7377   32.7377   33.7377   34.7377   35.7377   36.7377   37.7377

Visualize the third bond's cash flows (2.5 - 5 - 7.5 - 10) using the cfplot function.

cfplot(CDates(3,:),CFlows(3,:));
xlabel('Dates in Serial Number Format')
ylabel('Relative Amounts of Cash Flows')
title('CashFlow of 2.5 - 5 - 7.5 - 10 Stepped Coupon Bond')

Input Arguments

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Settlement date, specified either as a scalar or NSTP-by-1 vector of serial date numbers.

Settle must be earlier than Maturity.

Data Types: double

Maturity date, specified as a scalar or an NSTP-by-1 vector of serial date numbers representing the maturity date for each bond.

Data Types: double

Conversion dates, specified as a NSTP-by-max(NCONV) matrix containing conversion dates after Settle. The size of the matrix is equal to the number of instruments by the maximum number of conversions. Fill unspecified entries with NaN.

Data Types: double

Bond coupon rate, specified as an NSTP-by-max(NCONV+1) matrix containing coupon rates for each bond in the portfolio in decimal form. The matrix size is equal to the 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 CouponRates to reflect the same number of bonds. However, ConvDates has one less column than CouponRates. This situation is illustrated by

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

        Rate1               Rate2                 Rate3

Data Types: double

(Optional) Coupons per year, specified as an NSTP-by-1 vector. Values for Period are 1, 2, 3, 4, 6, and 12.

Data Types: double

(Optional) Day-count basis of each instrument, specified as an NSTP-by-1 vector.

  • 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 (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.

Data Types: double

(Optional) End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month having 30 or fewer days, specified for each bond as a nonnegative integer [0, 1] using a NSTP-by-1 vector.

  • 0 = Ignore rule, meaning that a payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

(Optional) Face value, specified for each bond as an NSTP-by-1 vector of nonnegative face values.

Data Types: double

Output Arguments

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Cash flow amounts, returned as a vector where the first entry in each row vector is the (negative) accrued interest due at settlement. If no accrued interest is due, the first column is zero.

Cash flow dates, returned as vector in serial date number form. At least two columns are always present: one for settlement and one for maturity.

Time factor for the SIA semiannual price/yield conversion, returned as a vector. The SIA semi-annual price/yield conversion is DiscountFactor = (1 + Yield/2).^(-TFactor). Time factors are in units of semiannual coupon periods. For ISMA conventions: DiscountFactor = (1 + Yield).^(-TFactor). Time factors are in units of annual coupon periods. In computing time factors, use SIA actual/actual conventions for all time factor calculations.

Note

For bonds with fixed coupons, use cfamounts. If you use a fixed-coupon bond with stepcpncfamounts, MATLAB® software generates an error.

Introduced before R2006a