liborprice

Price swap given swap rate

Syntax

Price = liborprice(ThreeMonthRates,Settle,Tenor,SwapRate)

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

Description

Price = liborprice(ThreeMonthRates,Settle,Tenor,SwapRate) computes the price per $100 notional value of a swap given the swap rate. A positive result indicates that fixed side is more valuable than the floating side.

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 Price Per $100 Notional Value of a Swap Given the Swap Rate

This example shows that a swap paying the par swap rate has a value of 0.

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

% compute the fixed rate from the Eurodollar data
FixedSpec = 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

% compute the price of a par swap
Price = liborprice(EDFutData(:,1:3), Settle, Tenor, FixedSpec.Coupon)

Price = 3.4694e-15

Price is effectively equal to 0.

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, liborprice 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

SwapRate — Swap rate

scalar decimal

Swap rate, specified as a scalar decimal.

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, liborprice 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

Price — Present value of the difference between floating and fixed-rate sides of the swap per $100 notional

numeric

Present value of the difference between floating and fixed-rate sides of the swap per $100 notional, returned as a numeric value.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although liborprice 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.