Rates

Vade's rates analytics cover interest rate curve construction, instrument pricing, risk sensitivities, and volatility products. Build discount and forward curves from market data, price linear and non-linear derivatives, and compute AD-powered greeks -- all from a single calibrated curve object.

What's Covered

• Curves -- DiscountCurve, ForwardCurve, LineCurve with configurable interpolation (log-linear, log-cubic, linear-zero)
• Parametric curves -- NelsonSiegel, NelsonSiegelSvensson, SmithWilson analytical models
• Linear instruments -- IRS, FRA, ZCS, OIS, Deposit, IRFuture
• Non-linear instruments -- CapFloor (caps and floors with Black-76 and Bachelier models)
• Calibration -- Multi-instrument Solver (Levenberg-Marquardt, Gauss-Newton, gradient descent) and single-curve bootstrap
• Risk -- AD-based delta, gamma, and tenor-bucketed sensitivities via IRImpliedCurve

Key Concepts

• Discount factor -- the present value of one unit of currency received at a future date, derived from the calibrated curve
• Forward rate -- the implied interest rate between two future dates, extracted from the discount curve
• Swap rate -- the fixed rate that makes an interest rate swap's NPV zero at inception
• Day count convention -- the rule for counting accrued days between dates (act360, act365f, 30360)
• Interpolation -- the method used to estimate discount factors between known curve nodes
• Bootstrap -- iterative node-by-node curve stripping using root-finding on each instrument in sequence
• Par rate -- the coupon rate at which an instrument prices to par (NPV = 0)
• Zero rate -- the continuously compounded rate implied by a single discount factor over a given tenor

Quick Taste

spot = float(calibrated.discount_factor(effective))
fwd_1y = float(calibrated.discount_factor(datetime.date(2026, 6, 16)))
# Discount factor decays from 1.0 as tenor increases
assert spot > fwd_1y

Guides

• Curve Building -- Interpolation method comparison and forward rate profiles from a calibrated DiscountCurve
• Bootstrap & Parametric Curves -- Node-by-node bootstrap via Brent root-finding and NelsonSiegel analytical models
• Pricing -- Price IRS, FRA, ZCS, OIS, and Deposit against calibrated curves
• Risk -- AD-based delta, gamma, and tenor-bucketed risk sensitivities
• Caps & Floors -- Cap and floor pricing with Black-76 and Bachelier volatility models

API Reference

• Curves -- DiscountCurve, LineCurve, ForwardCurve, parametric models (NelsonSiegel, SmithWilson)
• Instruments -- IRS, FRA, ZCS, OIS, Deposit, IRFuture, CapFloor
• Solver -- Multi-curve calibration, bootstrap, and Levenberg-Marquardt solver
• Cashflows -- Leg construction, period types, and accrual conventions