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fixedbyzero

Price fixed-rate note from set of zero curves

Syntax

[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity)
[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity,
Reset, Basis, Principal, EndMonthRule)
[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity,
Name, Value)

Description

[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity)
computes the price of a fixed-rate note from a set of zero curves. All inputs are either scalars or NINST-by-1 vectors unless otherwise specified. Any date may be a serial date number or date character vector. An optional argument may be passed as an empty matrix [].

[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity,
Reset, Basis, Principal, EndMonthRule)
computes the price of a fixed-rate note from a set of zero curves using optional input arguments. All inputs are either scalars or NINST-by-1 vectors unless otherwise specified. Any date may be a serial date number or date character vector. An optional argument may be passed as an empty matrix [].

[Price, DirtyPrice, CFlowAmounts, CFlowDates] =
fixedbyzero(RateSpec, CouponRate, Settle, Maturity,
Name, Value)
computes the price of a fixed-rate note from a set of zero curves with additional options specified by one or more Name, Value pair arguments.

Input Arguments

RateSpec

Structure containing the properties of an interest-rate structure. See intenvset for information on creating RateSpec.

CouponRate

Decimal annual rate.

Settle

Settlement date. Settle must be either a scalar or NINST-by-1 vector of serial date numbers or date character vectors of the same value which represent the settlement date for each bond. Settle must be earlier than Maturity.

Maturity

Maturity date.

Ordered Input or Name-Value Pair Arguments

Enter the following optional inputs using an ordered syntax or as name-value pair arguments. You cannot mix ordered syntax with name-value pair arguments.

Reset

NINST-by-1 vector representing the frequency of payments per year.

Default: 1

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 (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.

Default: 0 (actual/actual)

Principal

NINST-by-1 of notional principal amounts or NINST-by-1 cell array where each element is a NumDates-by-2 cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid.

Default: 100

EndMonthRule

End-of-month rule. A NINST-by-1 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

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

AdjustCashFlowsBasis

Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals.

Default: False

BusinessDayConvention

Require payment dates to be business dates. NINST-by-1 cell array with possible choices of business day convention:

  • actual

  • follow

  • modifiedfollow

  • previous

  • modifiedprevious

Default: actual

Holidays

Holidays used for business day convention. NHOLIDAYS-by-1 of MATLAB® date numbers.

Default: If no dates are specified, holidays.m is used.

Output Arguments

Price

A number of instruments (NINST) by number of curves (NUMCURVES) matrix of fixed-rate note prices. Each column arises from one of the zero curves.

DirtyPrice

A NINST-by-NUMCURVES matrix of dirty bond price (clean + accrued interest). Each column arises from one of the zero curves.

CFlowAmounts

A NINST-by-NUMCFS matrix of cash flows for each bond.

CFlowDates

A NINST-by-NUMCFS matrix of payment dates for each bond.

Examples

collapse all

This example shows how to price a 4% fixed-rate note using a set of zero curves by loading the file deriv.mat, which provides ZeroRateSpec, the interest-rate term structure needed to price the note.

load deriv.mat

CouponRate = 0.04;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';

Price = fixedbyzero(ZeroRateSpec, CouponRate, Settle, Maturity)
Price =

   98.7159

Assume that a financial institution has an existing swap with three years left to maturity where they are receiving 5% per year in yen and paying 8% per year in USD. The reset frequency for the swap is annual, the principals for the two legs are 1200 million yen and $10 million USD, and both term structures are flat.

Settle = datenum('15-Aug-2015');
Maturity = datenum('15-Aug-2018');
Reset = 1;

r_d = .09;
r_f = .04;

FixedRate_d = .08;
FixedRate_f = .05;

Principal_d = 10000000;
Principal_f = 1200000000;

S0 = 1/110;

Construct term structures.

RateSpec_d = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_d,'Compounding',-1);
RateSpec_f = intenvset('StartDate',Settle,'EndDate',Maturity,'Rates',r_f,'Compounding',-1);

Use fixedbyzero:

B_d = fixedbyzero(RateSpec_d,FixedRate_d,Settle,Maturity,'Principal',Principal_d,'Reset',Reset);
B_f = fixedbyzero(RateSpec_f,FixedRate_f,Settle,Maturity,'Principal',Principal_f,'Reset',Reset);

Compute swap price. Based on Hull (see References), a cross currency swap can be valued with the following formula V_swap = S0*B_fB_d.

V_swap = S0*B_f - B_d
V_swap =

   1.5430e+06

Related Examples

References

Hull, J. Options, Futures, and Other Derivatives. Prentice-Hall, 2011.

Introduced before R2006a

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