liborprice

Price swap given swap rate

Syntax

Price = liborprice(ThreeMonthRates,Settle,Tenor,SwapRate,StartDate,Interpolation,ConvexAdj,RateParam,InArrears,Sigma,FixedCompound,FixedBasis)

Arguments

ThreeMonthRates	Three-month Eurodollar futures data or forward rate agreement data. (A forward rate agreement stipulates that a certain interest rate applies to a certain principal amount for a given future time period.) An n-by-3 matrix in the form of [month year IMMQuote]. The floating rate is assumed to compound quarterly and to accrue on an actual/360 basis.
Settle	Settlement date of swap. Scalar.
Tenor	Life of the swap. Scalar.
SwapRate	Swap rate in decimal.
StartDate	(Optional) Scalar value to denote reference date for valuation of (forward) swap. This in effect allows forward swap valuation. Default = Settle.
Interpolation	(Optional) Interpolation method to determine applicable forward rate for months when no Eurodollar data is available. Default is 'linear' or 1. Other possible values are 'Nearest' or 0, and 'Cubic' or 2.
ConvexAdj	(Optional) Default = 0 (off). 1 = on. Denotes whether futures/forward convexity adjustment is required. Pertains to forward rate adjustments when those rates are taken from Eurodollar futures data.
RateParam	(Optional) Short-rate model's parameters (Hull-White) [a S], where the short-rate process is: $$dr=\left[\theta \left(t\right)-ar\right]dt+Sdz.$$ Default = [0.05 0.015].
InArrears	(Optional) Default = 0 (off). Set to 1 for on. If on, the routine does an automatic convexity adjustment to forward rates.
Sigma	(Optional) Overall annual volatility of caplets.
FixedCompound	(Optional) Scalar value. Compounding or frequency of payment on the fixed side. Also, the reset frequency. Default = 4 (quarterly). Other values are 1, 2, and 12.
FixedBasis	(Optional) Scalar value. Basis of the fixed side. 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.

Description

Price = liborprice(ThreeMonthRates,Settle,Tenor,SwapRate,StartDate,Interpolation,ConvexAdj,RateParam,InArrears,Sigma,FixedCompound,FixedBasis) 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 is the present value of the difference between floating and fixed-rate sides of the swap per $100 notional.

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 = datenum('15-Oct-2002');
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 = 2.7756e-15

Price is effectively equal to 0.