# getForwardRates

Get forward rates for input dates for IRDataCurve

## Description

example

F = getForwardRates(CurveObj,InpDates) computes discount factors for input dates for an IRDataCurve object. getForwardRates returns discrete forward rates for the intervals input into this function. For example, running the following code:

getForwardRates(irdc, {Date1, Date2, Date3})
gives three forwards rates and the three tenors are: [Settle, Date1], [Date1, Date2], and [Date2, Date3].

Note

The ratecurve object and the associated forwardrates were introduced in R2020a as part of a new object-based framework in the Financial Instruments Toolbox™ which supports end-to-end workflows in instrument modeling and analysis. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

F = getForwardRates(___,Name,Value) adds optional name-value pair arguments.

## Examples

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This example shows how to get forward rates for input dates for an IRDataCurve.

CurveSettle = datetime(2016,3,2);
Data = [2.09 2.47 2.71 3.12 3.43 3.85 4.57 4.58]/100;
Dates = datemnth(CurveSettle,12*[1 2 3 5 7 10 20 30]);
irdc = IRDataCurve('Zero',CurveSettle,Dates,Data);
getForwardRates(irdc, CurveSettle+30:30:CurveSettle+720)
ans = 24×1

0.0174
0.0180
0.0187
0.0193
0.0199
0.0205
0.0212
0.0218
0.0224
0.0230
⋮

Use getForwardRates to compute the forward rate from the Settle date to 5 years from March 1, 2017 and then the forward rate for the period from 5 years to 10 years from March 1, 2017.

Data = [2.09 2.47 2.71 3.12 3.43 3.85 4.57 4.58]/100;
Dates = daysadd(736755,[360 2*360 3*360 5*360 7*360 10*360 20*360 30*360],1);
irdc = IRDataCurve('Zero',today,Dates,Data);
getForwardRates(irdc,datemnth(irdc.Settle,12*[5 10]))
ans = 2×1

0.0399
0.0471

The first element (.0312) is the forward rate from the Settle to 5 years from March 1, 2017. The second rate (0.0458) is the forward rate for the period from 5 years to 10 years from March 1, 2017, in other words, the 5-year forward rate 5 years from March 1, 2017.

Use the following data to create an IRDataCurve object:

Data = [0.1 0.30 0.70 1.05 1.45 1.71 2.12 2.43 2.85 3.57]/100;
Settle = datetime(2016,8,8)
Settle = datetime
08-Aug-2016

Dates = datemnth(Settle,[3 6 9 12*[1 2 3 5 7 10 20]]);
irdc = IRDataCurve('Zero',Settle,Dates,Data)
irdc =
Type: Zero
Settle: 736550 (08-Aug-2016)
Compounding: 2
Basis: 0 (actual/actual)
InterpMethod: linear
Dates: [10x1 double]
Data: [10x1 double]

Compute the implied 6 month forward rates in 1 month, 2 months, and 3 months from the Settle date.

IntervalMonth = 6; % Interval for 6 month forward rates
FwdMonths = [1 2 3]'; % Starting in 1, 2, and 3 months from Settle
N = length(FwdMonths);
FwdRates_6M = zeros(N,1);

for k = 1:N
FwdDates = datemnth(irdc.Settle, [FwdMonths(k) FwdMonths(k)+IntervalMonth]);
f = getForwardRates(irdc,FwdDates);
FwdRates_6M(k) = f(2);
end

[FwdMonths FwdRates_6M]
ans = 3×2

1.0000    0.0050
2.0000    0.0074
3.0000    0.0101

## Input Arguments

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Interest-rate curve object, specified by using IRDataCurve.

Data Types: object

Input dates, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors. The input dates must be after the Settle date of IRDataCurve.

To support existing code, getForwardRates also accepts serial date numbers as inputs, but they are not recommended.

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: F = getForwardRates(irdc, CurveSettle+30:30:CurveSettle+720)

Compounding frequency per-year for forward rates, specified as the comma-separated pair consisting of 'Compounding' and a scalar numeric using one of the supported values:

• −1 = Continuous compounding

• 0 = Simple interest (no compounding)

• 1 = Annual compounding

• 2 = Semiannual compounding

• 3 = Compounding three times per year

• 4 = Quarterly compounding

• 6 = Bimonthly compounding

• 12 = Monthly compounding

Data Types: double

Day count basis for the forward rates, specified as the comma-separated pair consisting of 'Basis' and a scalar integer.

• 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

Data Types: double

## Output Arguments

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Forward rates, returned as a vector. getForwardRates returns forward rates corresponding to the periodicity of the dates input to getForwardRates. For example, where the dates are monthly, monthly forward rates are returned. The first element of the output is the forward rate from the Settle to one month, the second element is the forward rate from one month to two months, and so on.

## Version History

Introduced in R2008b

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