Fixed Income and Interest Rate Derivatives in ASRQuant

ASRQuant 1.2.0 preserves and exposes the rates stack through one namespace:

import asrquant as asr

asr.rates

Rates are decimals (0.025 == 2.5%) and times are year fractions unless dates are explicitly supplied.

Coverage map

Area	Main concepts	ASRQuant API
Conventions	ACT/360, ACT/365F, 30/360, 30E/360, maturity conversion	year_fraction, maturity_to_years, payment_schedule
Discounting	simple, periodic, continuous compounding	discount_factor, zero_rate_from_discount
Curves	discount, zero, forward, par, instantaneous forward	DiscountCurve, ForwardCurve
Bootstrapping	deposits, FRAs, swaps	bootstrap_discount_curve
Multi-curve	OIS discounting, tenor projection	MultiCurve, bootstrap_projection_curve_from_swaps
Curve models	Nelson-Siegel, Nelson-Siegel-Svensson	calibrate_nelson_siegel, calibrate_svensson
Bonds	coupon PV, clean/dirty, accrued interest	bond_price_from_curve, clean_price, dirty_price
Linear rates	FRA, futures, IRS, basis swap	fra_pv, rate_future_price, swap_pv, basis_swap_pv
RFR/OIS	overnight compounding, OIS par/PV	compounded_overnight_rate, ois_par_rate, ois_pv
Bond forwards	coupon carry and delivery forward value	bond_forward_price
Cross-currency	covered interest parity and terminal notional exchange	fx_forward_rate, cross_currency_zero_coupon_pv
Inflation	index-ratio annualization and ZC inflation swaps	zero_coupon_inflation_rate, zero_coupon_inflation_swap_pv
Risk	DV01, convexity, key-rate DV01	dv01, dollar_convexity, key_rate_dv01
Caps/floors	Black-76 and normal/Bachelier caplets, cap decomposition	caplet_price, cap_floor_price
Volatility	implied rate vol, caplet stripping	implied_rate_volatility, strip_caplet_volatilities
Swaptions	payer/receiver, Black and normal models	swaption_price
Smile	SABR/Hagan approximation and calibration	hagan_sabr_volatility, calibrate_sabr
Short-rate models	Vasicek, CIR, Hull-White, Ho-Lee, Black-Karasinski	corresponding model functions
Forward-rate models	one-factor HJM, terminal-measure LMM	hjm_one_factor_paths, lmm_terminal_measure_paths
Early exercise	generic scalar-state least-squares Monte Carlo	bermudan_lsm
Hedging/scenarios	parallel/slope/curvature and key-rate hedge solve	curve_scenario, key_rate_hedge
Calibration	SABR, Vasicek, Nelson-Siegel, Svensson	calibrate_*
Curve statistics	PCA, level/slope/curvature	yield_curve_pca, level_slope_curvature
Relative value	carry/roll-down	carry_roll_down
Model/data risk	no-arbitrage diagnostics, interpolation risk	no_arbitrage_curve_diagnostics, curve_interpolation_risk
Training	progressive exercises and curriculum	rates_curriculum, rates_exercises

Simple high-level lab

import asrquant as asr

lab = asr.RateQuantLab.from_zero_rates(
    [0.25, 0.5, 1, 2, 3, 5, 7, 10],
    [0.020, 0.021, 0.022, 0.023, 0.024, 0.026, 0.027, 0.028],
)

par = lab.par_swap(0, 5, frequency=2)
pv = lab.swap(0, 5, fixed_rate=0.025, notional=10_000_000)
checks = lab.diagnostics()

The lab is only a convenience layer. Every lower-level curve, convention and model remains directly accessible for research and validation.

ECB yield-curve data

provider = asr.ECBProvider()
history = provider.yield_curve_history(
    maturities=("3M", "6M", "1Y", "2Y", "5Y", "10Y", "30Y"),
    start="2020-01-01",
)

lab = asr.RateQuantLab.from_ecb()

yield_curve_history() converts percent-per-annum ECB observations into decimal rates and aligns maturities by timestamp.

Curve construction and model risk

A rates researcher should never evaluate only the fitted zero rates. ASRQuant exposes the induced forward curve and interpolation dispersion because small zero-rate differences can create large local forward differences.

risk = asr.curve_interpolation_risk(maturities, zero_rates)
print(risk[["maturity", "forward_dispersion"]])

For parametric curves:

fit_ns = asr.calibrate_nelson_siegel(maturities, zero_rates)
fit_svensson = asr.calibrate_svensson(maturities, zero_rates)

Compare RMSE, forward smoothness, stability through time and downstream pricing/risk—not RMSE alone.

Multi-curve valuation

Post-crisis rates valuation distinguishes the discount curve from projection curves. MultiCurve keeps this explicit. A projection curve can be implied from one curve for educational single-curve checks or bootstrapped separately from tenor swap quotes for multi-curve research.

Options and volatility

Rate options can be quoted in lognormal or normal volatility conventions. ASRQuant therefore keeps the model argument explicit rather than silently assuming Black.

black = asr.caplet_price(curve, 1.0, 1.5, 0.03, 0.20, model="black")
normal = asr.caplet_price(curve, 1.0, 1.5, 0.03, 0.01, model="normal")

The same principle applies to swaptions and implied-volatility inversion.

Models: what they are for

• Vasicek / CIR: tractable short-rate dynamics and term-structure intuition.
• Hull-White / Ho-Lee / Black-Karasinski: path simulation and comparative model research.
• HJM: forward-curve dynamics under no-arbitrage drift restrictions.
• LMM: correlated forward-rate dynamics on a tenor structure.
• SABR: smile representation/calibration for rate-option volatility research.

The implementations are transparent research/reference implementations. They are not a replacement for a desk's full conventions engine, collateral agreement model, market-calendar stack, exchange rulebook, or independently validated production pricer.

Risk and research

Core curve-risk work should include at least:

1. PV and par-rate checks;
2. parallel DV01;
3. key-rate DV01;
4. convexity/nonlinearity;
5. PCA level/slope/curvature shocks;
6. interpolation and curve-construction risk;
7. carry/roll decomposition;
8. model disagreement;
9. historical and scenario stress;
10. cross-currency/inflation/collateral assumptions when relevant;
11. early-exercise/model-regression diagnostics for Bermudan products;
12. reproducibility and convention audit.

Training path

asr.rates_curriculum()
asr.rates_exercises()

The exercise bank progresses from discounting and bootstrapping through multi-curve valuation, caps/floors, swaptions, SABR, short-rate models, HJM/LMM, curve PCA, interpolation risk and a complete ASR weekly publication cycle.