Interest Rates

The quantflow.rates module provides primitives for interest rate modelling: flat rates, yield curves, and curve fitting.

The central concept is the discount factor \(D_\tau\), the present value of one unit of currency paid at time \(\tau\). Every class in this module exposes a discount_factor method that computes \(D_\tau\) from the configured rate or curve.

Rate represents a spot or forward interest rate with a chosen compounding frequency (continuous by default) and day count convention. It supports continuous and periodic compounding and can be bootstrapped directly from a spot/forward pair.

YieldCurve is the abstract base for term-structure models. It defines the interface via discount_factor and instantaneous_forward_rate, with the two quantities linked by

\[\begin{equation} f(\tau) = -\frac{\partial \ln D_\tau}{\partial \tau} \end{equation}\]

Interpolated Curves build the term structure directly from observed zero rates at a set of anchor dates. InterpolatedLinearCurve interpolates the zero rate piecewise linearly, while InterpolatedMonotonicCubicCurve uses a shape-preserving cubic spline.

CIRCurve is a short-rate term-structure model derived from the Cox-Ingersoll-Ross process, with positive-rate dynamics and closed-form discount factors.

NelsonSiegelCurve is a concrete YieldCurve implementation that fits a smooth parametric curve to observed zero-coupon rates using the Nelson-Siegel functional form.

VasicekCurve is a Gaussian mean-reverting short-rate model with analytical formulas for discount factors and instantaneous forward rates.

Calibration provides YieldCurveCalibration, the base class for fitting a yield curve to discount factors, and OptionsDiscountingCalibration, which bootstraps asset and quote curves from put-call parity observations.