Future prices of Treasury bonds given current yield
[QtdFutPrice, AccrInt] = tfutbyyield(SpotCurve, Yield, SettleFut, MatFut,
ConvFactor, CouponRate, Maturity, Interpolation)
Treasury spot curve. A number of futures (NFUT)-by-3 matrix in the form of [SpotDates SpotRates Compounding].
Allowed compounding values are -1, 1, 2 (default), 3, 4, and 12, where -1 is continuous compounding.
Scalar or vector containing yield to maturity of bonds. Use bndyield for theoretical value of bond yield.
Scalar or vector of identical elements containing settlement date of futures contract.
Scalar or vector containing maturity dates (or anticipated delivery dates) of futures contract.
Conversion factor. See convfactor.
Scalar or vector containing underlying bond annual coupon in decimal.
Scalar or vector containing underlying bond maturity.
(Optional) Interpolation method. Available methods are (0) nearest, (1) linear, and (2) cubic. Default = 1. See interp1 for more information.
Inputs (except SpotCurve) must either be a scalar or a vector of size equal to the number of Treasury futures (NFUT) by 1 or 1-by-NFUT.
[QtdFutPrice, AccrInt] = tfutbyyield(SpotCurve, Yield, SettleFut, MatFut, ConvFactor, CouponRate, Maturity, Interpolation) computes future prices of Treasury notes and bonds given current yields of Treasury bonds/notes. The output arguments are:
QtdFutPrice — Quoted futures price, per $100 notional.
AccrInt — Accrued Interest due at delivery date, per $100 notional.
In addition, you can use the Financial Instruments Toolbox™ method getZeroRates for an IRDataCurve object with a Dates property to create a vector of dates and data acceptable for tfutbyyield. For more information, see Converting an IRDataCurve or IRFunctionCurve Object.
This example shows how to determine the future price of two Treasury bonds based upon a spot rate curve constructed from data for November 14, 2002.
% construct spot curve from Nov 14, data Bonds = [datenum('02/13/2003'), 0; datenum('05/15/2003'), 0; datenum('10/31/2004'), 0.02125; datenum('11/15/2007'), 0.03; datenum('11/15/2012'), 0.04; datenum('02/15/2031'), 0.05375]; Yields = [1.20; 1.25; 1.86; 2.99; 4.02; 4.93]/100; Settle = datenum('11/15/2002'); [ZeroRates, CurveDates] = ... zbtyield(Bonds, Yields, Settle); SpotCurve = [CurveDates, ZeroRates]; % calculate a particular bond's future quoted price RefDate = [datenum('1-Dec-2002'); datenum('1-Mar-2003')]; MatFut = [datenum('15-Dec-2002'); datenum('15-Mar-2003')]; Maturity = [datenum('15-Aug-2009');datenum('15-Aug-2010')]; CouponRate = [0.06;0.0575]; ConvFactor = convfactor(RefDate, Maturity, CouponRate); Yield = [0.03576; 0.03773]; Interpolation = 1; [QtdFutPrice, AccrInt] = tfutbyyield(SpotCurve, Yield, Settle, ... MatFut, ConvFactor, CouponRate, Maturity, Interpolation)
QtdFutPrice = 114.0416 113.4034 AccrInt = 1.9891 0.4448