SwapsQuantLib

A compact Python library for swap curve construction, discount curve calibration, and pricing using automatic differentiation with dual numbers.

Features

• Calibrate discount curves to objective rates (liquid market swap rates) using:
  • gradient_descent
  • gauss_newton
  • levenberg_marquardt
• Interpolation modes:
  • Log-linear (flat between knots, step-wise)
  • Linear (piecewise linear with elbows at knots)
  • Mixed (cubic B-spline + log-linear fallback before first knot)
• Turns and Curvature constraints support via SwapSpread instruments
• Weighted optimization, pass weights to prefer repricing some instruments over others
• Layered curves, caliberate using some instruments and then recaliberate with additional instrume
• Risk: Risk using automatic Differentiation via custom Dual numbers to compute sensitivities and optimize efficiently.
• Swap and schedule support: build payment dates, fixed/float legs, and par-rate computations.

Curve calibration and swap outputs

• Log-linear gives a flat rate between knots (step shape).
• Linear gives an upward slope between knots (straight line segments).
• Mixed gives a smooth curve between knots (B-spline) and falls back to log-linear before the first knot.

Layered curve with Mixed cubic interpolation, turns and curvature constraints

• 1st-layer is built with Turns on meeting dates
• Curvature constraint enforced as 2nd derivative = 0 on MPC dates via SwapSpread(SwapSpread(mpc_1, mpc_2), SwapSpread(mpc_2, mpc_3)): 0
• 2nd-layer swaps from 4y, 6y, 8y, 9y, 12y, 35y (skew adjustments on long end) are added using:
  • skews_layer_2 = {Swap(...): value, ...}

3Y O/N RFR curve (mixed interpolation)

10Y curve example

Curves with turns on certain dates using SwapSpread instruments

• Use SwapSpread instrument to specify -0.25bp turn on 31-12-2022 and 30-06-2023

Log-linear SONIA curves with turns and curvature constraints

• Turns on meeting dates
• Curvature constraint enforced as 2nd derivative = 0 on MPC dates via SwapSpread(SwapSpread(mpc_1, mpc_2), SwapSpread(mpc_2, mpc_3)): 0

No curvature constraints

With curvature constraints

B-spline implementation (visible, all key plots)

• B-spline basis generation (orders 1–4)
• Repeated knot handling (smoothness reduction as expected)
• Derivative evaluation for B-spline curves

Plot: B-splines (repeated knots)

Plot: B-splines (no repeats)

Plot: B-spline derivative (order 4)

How to run tests

• Schedule path generation
  • python -m tests.schedule_test
• Swap pricing and swap curve tests
  • python -m tests.swap_test
  • python -m tests.swap_dual_curve_test
• Dual number unit tests
  • python -m tests.dual_test
• Solved curve & calibration tests
  • python -m tests.solvedcurve_test
• B-spline plots
  • python -m tests.bspline_plot

Notes

• This repo is a functional prototype focused on curve construction and calibration; it is not intended as a production-grade implementation.
• Reference: "Pricing and Trading Interest Rate Derivatives" by JHM Darbyshire.