liborfloat2fixed

Compute par fixed-rate of swap given 3-month LIBOR data

Syntax

[FixedSpec,ForwardDates,ForwardRates] = liborfloat2fixed(ThreeMonthRates,Settle,Tenor)

Price = liborprice(___,StartDate,Interpolation,ConvexAdj,RateParam,InArrears,Sigma,FixedCompound,FixedBasis)

Description

[FixedSpec,ForwardDates,ForwardRates] = liborfloat2fixed(ThreeMonthRates,Settle,Tenor) computes forward rates, dates, and the swap fixed rate.

Note

The liborfloat2fixed function assumes that floating-rate observations occur quarterly on the third Wednesday of a delivery month. The first delivery month is the month of the first third Wednesday after Settle. Floating-side payments occur on the third-month anniversaries of observation dates. Fixed payments start on the same date as the first floating payment, and recur on the same date as the first-coupon date (on anniversary months).

Price = liborprice(___,StartDate,Interpolation,ConvexAdj,RateParam,InArrears,Sigma,FixedCompound,FixedBasis) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Compute the Par Fixed-Rate of a Swap Given 3-Month LIBOR Data

This example shows how to compute the par fixed-rate of a swap given 3-month LIBOR data. Use the supplied EDdata.xls file as input to a liborfloat2fixed computation.

[EDFutData, textdata] = xlsread('EDdata.xls');
Settle                = datetime(2002,10,15);
Tenor                 = 2;

[FixedSpec, ForwardDates, ForwardRates] =... 
liborfloat2fixed(EDFutData(:,1:3), Settle, Tenor)

FixedSpec = struct with fields:
      Coupon: 0.0222
      Settle: '16-Oct-2002'
    Maturity: '16-Oct-2004'
      Period: 4
       Basis: 1

ForwardDates = 8×1

      731505
      731596
      731687
      731778
      731869
      731967
      732058
      732149

ForwardRates = 8×1

    0.0177
    0.0166
    0.0170
    0.0188
    0.0214
    0.0248
    0.0279
    0.0305

Input Arguments

ThreeMonthRates — Three-month Eurodollar futures data or forward rate agreement data

matrix

Three-month Eurodollar futures data or forward rate agreement data, specified as an N-by-3 matrix in the form of [month year IMMQuote]. A forward rate agreement stipulates that a certain interest rate applies to a certain principal amount for a given future time period. The floating rate is assumed to compound quarterly and to accrue on an actual/360 basis.

Data Types: double

Settle — Settlement date of fixed-rate of swap

datetime scalar | string scalar | date character vector

Settlement date of fixed-rate of swap, specified as a scalar datetime, string, or date character vector.

To support existing code, liborfloat2fixed also accepts serial date numbers as inputs, but they are not recommended.

Tenor — Life of the swap contract

scalar integer

Life of the swap contract, specified as a scalar integer.

Data Types: double

StartDate — Reference date for valuation of forward swap

Settle (default) | datetime scalar | string scalar | date character vector

(Optional) Reference date for valuation of forward swap, specified as a scalar datetime, string, or date character vector. This in effect allows forward swap valuation.

To support existing code, liborfloat2fixed also accepts serial date numbers as inputs, but they are not recommended.

Interpolation — Interpolation method to determine applicable forward rate for months when no Eurodollar data is available

'linear' (1) (default) | scalar integer with value of 0, 1, or 2

(Optional) Interpolation method to determine applicable forward rate for months when no Eurodollar data is available, specified as a scalar numeric with values of:

• 0 is 'nearest'

• 1 is 'linear'

• 2 is 'cubic'

.

Data Types: double

ConvexAdj — Indicates whether futures/forward convexity adjustment is required

0 (off) (default) | scalar logical with a value of 0 or 1

(Optional) Indicates whether futures/forward convexity adjustment is required, specified as a scalar logical. Use ConvexAdj for forward rate adjustments when those rates are taken from Eurodollar futures data.

Data Types: logical

RateParam — Short-rate model's parameters (Hull-White)

[0.05 0.015] (default) | vector

(Optional) Short-rate model's parameters (Hull-White), specified a 1-by-2 vector to denote the parameters [a S], where the short-rate process is:
$$dr=\left[\theta \left(t\right)-ar\right]dt+Sdz.$$

Data Types: double

InArrears — Indicates whether the swap is in arrears

0 (off) (default) | scalar logical with a value of 0 or 1

(Optional) Indicates whether the swap is in arrears, specified as a scalar logical.

Data Types: logical

Sigma — Overall annual volatility of caplets

scalar numeric

(Optional) Overall annual volatility of caplets, specified as a scalar numeric.

Data Types: double

FixedCompound — Compounding or frequency of payment on the fixed side

4 (quarterly) (default) | scalar numeric with possible values of 1, 2,4, or 12

(Optional) Compounding or frequency of payment on the fixed side, specified as a scalar numeric with one of the following possible values:

• 1 is annual

• 2 is semiannual

• 4 is quarterly

• 12 is monthly

Data Types: double

FixedBasis — Basis of the fixed side

0 (actual/actual ) (default) | scalar numeric

(Optional) Basis of the fixed side, specified as a scalar numeric using one of the supported values:.

• 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)

For more information, see Basis.

Data Types: double

Output Arguments

FixedSpec — Structure of the fixed-rate side of the swap

structure

Structure of the fixed-rate side of the swap, returned as a structure with the following fields:

• Coupon: Par-swap rate

• Settle: Start date

• Maturity: End date

• Period: Frequency of payment

• Basis: Accrual basis

ForwardDates — Dates corresponding to ForwardRates

numeric

Dates corresponding to ForwardRates, returned as datetime numbers. All of the dates are third Wednesdays of the month, spread three months apart. The first element is the third Wednesday immediately after Settle.

ForwardRates — Forward rates corresponding to the forward dates

numeric

Forward rates corresponding to the forward dates, quarterly compounded, and on the actual/360 basis, returned as numeric decimal values.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although liborfloat2fixed supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.