Zero Curve

Construct and analyze zero curves

A zero curve is a special type of yield curve that maps interest rates on zero-coupon bonds to different maturities across time. Zero-coupon bonds have a single payment at maturity, so these curves enable you to price arbitrary cash flows, fixed-income instruments, and derivatives. Another type of interest rate curve, the forward curve, is constructed using the forward rates derived from this curve.

Bootstrapping an interest rate curve using the zero and forward curves.

Zero curves are separately constructed for government securities and for inter-bank markets.

Zero-coupon bonds are available for a limited number of maturities, so you typically construct zero curves with a combination of bootstrapping and interpolation techniques in order to build a continuous curve. Once you construct these curves, you can then use them to derive other curves such as the forward curve and to price financial instruments.

Leading financial institutions use MATLAB to build and analyze these curves. MATLAB toolboxes such as those for finance, data feeds, financial instruments, statistics, and curve fitting support curve construction tasks, enabling you to:

• Construct curves by bootstrapping and interpolation
• Price financial instruments based on discount factors implied by the curve
• Derive instantaneous forward curves for OTC derivatives pricing

Examples and How To

• UniCredit Bank Austria Develops an Enterprise-Wide Market Data Engine (User Story)
• Yield Curve Forecasting with the Diebold-Li Model (Example)
• Prepayment Modeling with a Two-Factor Hull-White Model (Example)
• Sensitivity of Bond Prices to Parallel Shifts in the Yield Curve (Example)
• Term Structure Analysis and Interest Rate Swap Pricing (Example)
• Analysis of Inflation Indexed Instruments (Example)

Software Reference

• Pricing and Computing Yields for Fixed-Income Securities (Documentation)
• Deriving an Implied Zero Curve (Documentation)
• Discount Curve Given Zero Curve (Function)
• Forward Curve Given Zero Curve (Function)
• Bond Key Rate Duration Given Zero Curve (Function)
• Zero Curve Bootstrapping from Coupon Bond Data Given Price (Function)

See also: swap curve, yield curve, Financial Toolbox, Econometrics Toolbox, Parallel Computing Toolbox, Global Optimization Toolbox, Neural Network Toolbox,  Curve Fitting Toolbox, Datafeed Toolbox, Statistics Toolbox, Financial Instruments Toolbox