TheQuantBateman

01

INTUITION

Separate the quote from the quantity inferred from it.

A portfolio does not own ‘duration’ in the abstract. It owns sensitivity to specific curve inputs, dates and curve roles; as time passes, cash flows roll through that geometry even if market quotes do not move.

01

DV01 must state whether rates are bumped up or down and whether it is PV change or signed derivative.

02

Key-rate risk depends on bump shape and curve rebuild policy.

03

Carry and roll-down are scenario P&L under a frozen-market assumption, not guaranteed return.

02

WHY MARKETS CARE

Start from executable inputs and conventions.

Trading limits, hedge sizing, P&L explanation and macro scenario design require exposures that map back to liquid curve instruments.

INSTRUMENTS

swaps and futures

government bonds

basis swaps

options on rates

QUOTE CONVENTION

Report currency, valuation date, curve role, quote set, bump direction/size, rebuild mode and units. One basis point is 0.0001 in decimal rates.

03

MATHEMATICS

Transform quotes without losing units or arbitrage constraints.

Formula · Short derivation

Signed quote DV01

DV01_i=V(q_i+h)-V(q_i)

This convention reports PV change for a +1bp quote bump; many desks use the negative or symmetric derivative, so sign must be stated.

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Short derivation

From curve-node shocks to liquid hedge ratios

Differentiate the entire calibration-and-pricing pipeline with respect to market quotes, not only internal zero nodes.

01
Freeze the market state
Store quote snapshot, curve policy, trade state and base PV.
02
Bump one liquid quote
Move q_i by h, rebuild every dependent curve and reprice the portfolio.
03
Record the signed PV change
Retain V(q_i+h)−V(q), the bump size and the affected curve role.
04
Assemble scenario vectors
Combine quote DV01s with level, slope or butterfly shock vectors while keeping units consistent.
$\Delta V_{lin}=J_q\Delta q$
05
Validate nonlinearity
Compare up/down symmetric bumps and full revaluation under larger scenarios.
Numerical checkThe sum of bucketed first-order contributions should reconcile with a parallel small-bump PV change within curvature tolerance.

Curve risk is a Jacobian from liquid market quotes to portfolio value, augmented by nonlinear scenarios and time-passage attribution.

Inputs

V(q): portfolio PV from market quotes
DV01_i: i-th quote sensitivity
h=10^{-4}: one-bp bump
\Delta t: carry horizon

Assumptions and limits

Finite differences mix model nonlinearity with rebuild effects.
Key-rate results depend on interpolation and bump localisation.
Frozen-curve carry omits future market moves, funding and execution costs.

Formula · Short derivation

First-order scenario P&L

\Delta V\approx\sum_i\frac{\partial V}{\partial q_i}\Delta q_i

Quote-space gradients map a prescribed level, slope or butterfly move into approximate P&L.

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Formula · Short derivation

Carry/roll decomposition

\Delta V_{frozen}=\Theta_{carry}\Delta t+\Delta V_{roll}+\Delta V_{cash}

Under a frozen curve, accrual, curve roll and realised cash flows are separated for attribution.

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05

MODEL / PRICING

Invert, fit, and reprice the market instruments.

METHOD

Bump liquid calibration quotes, rebuild all dependent curves and return signed quote-space risk plus internal node diagnostics and full-revaluation scenarios.

CALIBRATION

Use stable bump sizes, symmetric checks and a frozen dependency graph. Version curve construction alongside risk results.

Implementation with current QuantLib

Relink or rebuild quote handles one at a time and force dependent term structures to update before repricing. Preserve base/bumped snapshots; validate quote-space risk against analytical cash-flow sensitivities where available.

API authority: upstream QuantLib reference pinned in the source registry.

06PYTHON IMPLEMENTATIONOpen the implementation and checks.

ARCHITECTURE

Keep market conventions and quote lineage at the boundary.
Solve curves and dynamics in framework-free deterministic kernels.
Return residuals, state and sensitivities with every value.
Test analytical limits, reconstruction identities and failure domains.

PYTHON 3 · NUMPY / SCIPY

Parallel and key-rate DV01

Compute signed +1bp PV changes and reconcile the bucket sum with a parallel bump.

REUSABLE EXAMPLE

01from __future__ import annotations

02

03import math

04

05times = [1., 2., 5., 10., 20.]

06cashflows = [2., 2., 2., 2., 102.]

07rates = [0.03, 0.032, 0.035, 0.038, 0.04]

08h = 1e-4

09

10def pv(curve: list[float]) -> float:

11 return sum(c*math.exp(-r*t) for c, r, t in zip(cashflows, curve, times))

12

13base = pv(rates)

14buckets = []

15for i in range(len(rates)):

16 bumped = rates.copy(); bumped[i] += h

17 buckets.append(pv(bumped) - base)

18parallel = pv([r+h for r in rates]) - base

19assert abs(sum(buckets) - parallel) < 0.01

20assert all(x < 0 for x in buckets)

21print(f"parallel +1bp={parallel:.6f}")

07

INTERACTIVE LAB

Move the quote and inspect every linked representation.

QUOTE-SPACE DV01 AND CURVE FACTORS

Key-rate and scenario laboratory

Apply parallel, steepener, flattener and butterfly shocks; inspect bucketed DV01, carry and roll-down.

SYNTHETIC · CONTROLLED SCENARIOS

SCENARIO INTENSITY70%

Net DV01-752.6

Full scenario P&L-18816

Largest bucket7Y

PV / DV01 (currency units) by Key-rate tenor (years)

Parallel +25bp: Level factor.

DV01
scenario P&L / 10

Key-rate tenor (years): 0.5Y. DV01: -1.1 CU. scenario P&L / 10: -2.9 CU.

Use Left/Right or Up/Down arrows to inspect values; Home and End jump to the bounds.

08

FRONT OFFICE

Where the model meets the book.

ON THE DESK

“A DV01 without curve role, bump sign and rebuild policy cannot be hedged or reconciled.”

VISIBLE INPUTS

portfolio cash flows

market quote set

curve dependency graph

bump policy

carry horizon

CALIBRATION

Risk must use the same accepted curve build as valuation; symmetric and parallel-reconciliation tests are release gates.

RISK

level/slope/butterfly

key-rate concentration

carry/roll

basis and convexity

DAILY WORKFLOW

freeze base PV
bump/rebuild
aggregate buckets
run full scenarios
attribute carry and market move

Production failure modes

mixed DV01 signs
partial dependency rebuild
bump too small/large
risk reported in internal nodes only

09MACRO CONNECTIONOpen the transmission channel.

MACRO CONNECTION

Macro scenarios as curve-factor shocks

Policy, inflation, growth and supply shocks rarely move every tenor equally; level, slope and butterfly factors connect narratives to portfolio P&L.

01Macro thesistransmits

defines tenor-specific shock

02Curve factorstransmits

encode level/slope/butterfly

03Quote sensitivitiestransmits

map shock into PV

04Hedge decisionoutput

targets residual factor risk

10COMMON PITFALLSOpen the failure checklist.

01

Calling PV change for +1bp ‘DV01’ without sign definition.

02

Summing risks across currencies without FX and units.

03

Computing node risk without rebuilding calibrated curves.

04

Treating carry as a forecast-free profit.

11SOURCES / FURTHER READINGOpen sources and continue the track.

research

Curve construction, multi-curve, short-rate and HJM lectures

Research map for term-structure theory and numerical experiments; all platform explanations and code are original.

Source: Financial Engineering: Interest Rates & xVA
Author: L. A. Grzelak
Ref: main

OPEN ORIGINAL SOURCE ↗

research

Monte Carlo, stochastic calculus and calibration lectures

Mathematical and numerical cross-reference for model dynamics and diagnostics.

Source: Computational Finance Course
Author: L. A. Grzelak
Ref: main

OPEN ORIGINAL SOURCE ↗

implementation reference

Current bootstrapping, interpolation, curve, model, cap/floor and swaption tests

Implementation authority for production object boundaries and regression-test patterns.

Source: QuantLib upstream
Author: QuantLib contributors
Ref: v1.42.1

OPEN ORIGINAL SOURCE ↗

From curve-node shocks to liquid hedge ratios

Freeze the market state

Bump one liquid quote

Record the signed PV change

Assemble scenario vectors

Validate nonlinearity

Macro scenarios as curve-factor shocks

Curve construction, multi-curve, short-rate and HJM lectures

Monte Carlo, stochastic calculus and calibration lectures

Current bootstrapping, interpolation, curve, model, cap/floor and swaption tests