MuniBondPricing

Getting StartedExpand or collapse

Typical Workflow for Single Bond Pricing

Define the bond features—Issue Date, Settlement, Maturity, Set Call Date (if desired), and Coupon Rate—in Step 1 below.
Select a baseline Treasury curve in Step 2 below.
Set and apply adjustment factors to create the initial municipal pricing rates in Step 3 below.
Review the rates using the Rate Chart or Rate Table.
Press Calculate or enable Live Recalc above.
Review the results in Bond Analytics and Call Option Modeling.

Notes

The displayed bond price uses the Municipal Pricing Rates shown in the tables and charts. Individual spot rates may be adjusted directly using the left sidebar or on the chart. Curve-based rates may differ from the pricing rates, and the pricing rates can be snapped to the model curves.
The bond may be priced with or without a call option. Call-option valuation is performed using the Call Option Modeling tab.
When Live Recalc is enabled, prices and analytics update automatically, and the Calculate button is disabled (grayed out). When Live Recalc is disabled, use Calculate to recompute the bond price and analytics after changing spot rates or bond features.
The Maturity Ladder tab provides separate instructions and calculations for pricing a series of bonds across multiple maturities.

STEP 1

Set Bond Features

STEP 2

Select a Starting Treasury Curve

Choose a starting Treasury curve. The selected curve populates the Treasury Spot Rates and the Direct Treasury Rate inputs in the left sidebar.

Pick Historical Rate Curve Latest available date: IMPORT CSV

Historical curve

The historical selector is populated from historical_yields2.csv.

Other Curves

Flat Treasury Rate Value: % Normal Treasury Rate Curve 10-Year Rate: % Humped Treasury Rate Curve 10-Year Rate: % 1-Year Rate: % Inverted Treasury Rate Curve 10-Year Rate: % 1-Year Rate: %

Note: Picking a historical or other curve immediately repopulates the Direct Treasury Rate method.

STEP 3

Derive Municipal Pricing Rates from Treasury Rates

Use one implied tax rate and/or spread adjustment Set implied tax rate and/or spread adjustment for tenors below

Implied Tax Rate (%) Spread Adjustment (%)

For each tenor: Municipal Pricing Rate = Treasury Rate × (1 − implied tax rate) + spread adjustment. The spread may be positive or negative and may be used by itself by setting the implied tax rate to 0%.

Derived Municipal Rates (Standard Tenors)

3M (%) 6M (%) 1Y (%) 2Y (%) 3Y (%) 5Y (%) 7Y (%) 10Y (%) 20Y (%) 30Y (%)

Note: See the Rate Chart tab for a visual display of the term structure.

RATE CHART

Treasury and Municipal Spot Curves

Treasury Spot RatesTreasury ModelMunicipal Pricing RatesMunicipal Model

INITIALIZING MARKET DATA…

GRID MAX MATURITY Y-AXIS MIN YIELD MAX YIELD

RATE TABLE

Municipal and Treasury Curve Worksheet

Table Number Size

Tenor	Maturity	Municipal Pricing Rate	Municipal Model Rate	Treasury Spot Rate	Treasury Model Spot	Municipal/Treasury Ratio	Implied Tax Rate	Discount Factor	Forward Rate

PUBLIC AND LICENSED BENCHMARKS

Market Data

PARTIALLY IMPLEMENTED

Source	Available Without a Subscription	Access	Best Use in This Application
FRED Federal Reserve Bank of St. Louis	Current Treasury market series and many downloadable interest-rate series through web pages and the FRED API. FRED also contains legacy historical municipal series, including the Municipal Twenty-Bond Average, but not a current full AAA municipal curve.	Public Open FRED	Automated Treasury baseline rates; historical comparisons; recession and macro context.
Federal Reserve Board H.15 and Financial Accounts	Current H.15 selected interest rates, including Treasury maturities, plus Z.1 municipal-securities amounts outstanding. The Board does not publish a daily municipal benchmark yield curve.	Public Open H.15 downloads	Direct official Treasury inputs and municipal-market size statistics.
MSRB EMMA Electronic Municipal Market Access	Official statements, continuing disclosures, security and issue details, CUSIP search, and publicly reported municipal trade history including transaction prices, yields, dates, and trade sizes.	Public Open EMMA	Best public source for individual municipal bond disclosures and reported trades. Useful for manually identifying an observed price or yield, but it does not provide an unrestricted real-time evaluated-pricing API for automated redistribution.
ICE Data Indices	Public descriptions, methodology, commentary, and occasional published snapshots of ICE municipal benchmarks. Full evaluated municipal curves, security-level pricing, and production data feeds are licensed products.	Limited public View ICE muni information	Benchmark comparison when a public snapshot is available; not a dependable free automated curve feed.
SIFMA Municipal Swap Index	Public methodology and explanatory material for the weekly seven-day high-grade tax-exempt VRDO index. The index is calculated and published by Bloomberg, so current-value access and redistribution may be restricted.	Methodology public View SIFMA index guide	Short-term tax-exempt benchmark entered manually when a current published value is available.
SIFMA Municipal Statistics	Downloadable issuance, trading-volume, outstanding, holder, maturity, coupon, tax-status, and callable-status statistics. These are market-activity statistics rather than daily pricing curves.	Public Open municipal statistics	Market overview, issuance trends, trading activity, and research context.
MMD / TM3 LSEG Municipal Market Data	Product descriptions and selected commentary may be public. The MMD AAA scale, additional rating curves, real-time data, analytics, and feeds are subscription services.	Subscription View TM3 product page	Industry-standard benchmark only when the user or organization has licensed access.
Refinitiv / LSEG Pricing	Public product information and occasional research articles. Evaluated municipal prices, descriptive data, yield curves, and security-level feeds require a commercial license.	Subscription View pricing product	Security-level evaluated prices and curves when licensed; otherwise informational only.
The Bond Buyer	Some public or metered market articles report delayed snapshots of MMD, ICE, S&P, and Bloomberg BVAL scales and discuss the Bond Buyer 20-Bond Index. Access varies by article, and there is no stable unrestricted public pricing API.	Public / metered Open The Bond Buyer	Manual benchmark checks and market commentary; not suitable as an automated production feed.

Access classification reviewed July 17, 2026. Source terms, paywalls, and redistribution rights can change.

NON-CALLABLE BOND

Basic Analytics

The basic analytics below are based on the non-call version of the bonds and do not fully account for the technical effects of accrued interest, day-count conventions, and other real-world aspects of bond pricing, including the distinction between clean and dirty prices. They may not match exactly the QuantLib-based calculations shown in other tabs.

VALUATION SUMMARY

Price and Risk Measures

MeasureMunicipalTreasury

Price——

YTM——

Modified Duration——

Convexity——

DV01 (per $100)——

$100 face · Semiannual coupon · Coupon rate: — · Maturity date: — · Original term: — · Remaining term: —

Duration is in years; convexity is in years². DV01 estimates the price increase from a one-basis-point decline in yield per $100 face value.

PRICE SENSITIVITY

Price–Yield Relationship

The same non-callable bond cash flows repriced around the Municipal and taxable Treasury YTMs.

Because the Municipal and Treasury valuations use the same non-callable bond cash flows, their price-versus-YTM curves coincide. The wide blue Municipal line is shown beneath the dashed black Treasury line; the separate valuation markers identify each curve-based YTM and price.

QUANTLIB-PYTHON

Call Option Modeling

Black–Karasinski one-factor lattice

This tab shows call option valuation results that are based on QuantLib calculations, using the municipal zero curve and the bond call assumptions below. Select either the Hull–White or Black–Karasinski one-factor short-rate lattice method and the associated volatility parameter. The issuer call option value is the difference between the non-callable and callable model values.

QUANTLIB BACKEND

Callable-Bond Valuation

Call DateNone

Set / Change Call Date Linked to Getting Started

Short-Rate Model Call Price Mean Reversion (a) Volatility (σ) Tree Steps

CALL OPTION METRICS

Callable-Bond Decision Summary

PARTIALLY IMPLEMENTED

Observed Market Input

Observed Input Observed Clean Price

A single issuer-focused summary of the current QuantLib callable-bond valuation. Metrics not yet produced by the model are identified as not calculated.

Metric	Value
Callable Price	—
Equivalent Noncall Price	—
Embedded Call Option Value	—
Yield to Call (YTC)	—
Yield to Maturity (YTM)	—
Probability of Call	Not calculated
Effective Duration	—
Effective Convexity	—
Observed Clean Price	—
Model-Implied Issuer OAS	—
Observed Price / YTC OAS	—
Expected Call Year	—
Break-even Refunding Yield	Not calculated

MODEL: BLACK–KARASINSKI 1F

MORE CALL ANALYSIS

Scenario and Interest-Rate Tree Analysis

Use the Additional Call Analysis tab for parallel-rate scenarios, call-option-value charts, and a model-specific short-rate tree visualization.

ISSUER CALL ANALYTICS

Additional Call Analysis

Uses the selected call-valuation model

This tab extends the QuantLib callable-bond valuation with bond-specific interest-rate scenarios, OAS sensitivity, and a sampled view of the short-rate lattice implied by the selected model, municipal curve, mean reversion, volatility, and valuation horizon. The full QuantLib pricing lattice continues to use the selected number of time steps.

MODEL SCENARIOS

Call Option Interest-Rate Scenarios

Reprice the currently selected bond and call structure under parallel shifts to the Municipal Pricing Rate curve. Scenario analysis is intentionally manual and is not triggered by Live Recalc.

Manual scenarios: −200, −100, −50, 0, +50, +100, and +200 basis points.

Table Number Size

Curve Shift	Callable Price	No-Call Price	Call Option Value	Callable YTM	No-Call YTM
Select Calculate Scenarios to run the manual analysis.

MODEL SENSITIVITY

OAS and Volatility

For each volatility assumption, the app calculates the positive parallel shift to the Municipal Pricing Rate curve that makes the non-callable bond price equal the callable model price. This manual analysis can be calculation intensive.

Uses a model-appropriate volatility range.

MODEL LATTICE

Interest-Rate Tree

A sampled recombining tree generated from the selected short-rate model and current valuation inputs. Node labels show modeled annualized short rates; the range below reports the true minimum and maximum of the displayed nodes.

Model: Black–Karasinski 1FDisplayed periods: 6Displayed rate range: —QuantLib valuation steps: 300

QUANTLIB MATURITY ANALYSIS

Bond Maturity Ladder

Enter the 11 standard-tenor municipal spot rates in the left sidebar. After you select Calculate, an NSS curve is fitted, a full monthly zero curve is built through 30 years, and QuantLib values eligible bonds with maturity dates from 1 through 30 years after the Issue Date.

BOND AND MODEL INPUTS

Bond Parameters

Dates

Issue Date Settlement Date

Set Call Date 10 Years after Issuance

Bond Parameters

Coupon Rate (%) Call Price

Interest Rate Model

Model Mean Reversion Volatility Tree Steps

RATE AND YIELD PROFILE

Spot Rate and YTM or YTC by Maturity

QUANTLIB RESULTS

Prices and Yields by Maturity

Table Number Size

Maturity (Years)	Price	YTM/YTC	Non-Callable Price	No-Call YTM	Call Option Value
Select Calculate to value the maturity ladder.

Municipal Bonds

Typical Workflow for Single Bond Pricing

Notes

Set Bond Features

Select a Starting Treasury Curve

Other Curves

Derive Municipal Pricing Rates from Treasury Rates

Derived Municipal Rates (Standard Tenors)

Treasury and Municipal Spot Curves

Municipal and Treasury Curve Worksheet

Market Data

Basic Analytics

Price and Risk Measures

Price–Yield Relationship

Call Option Modeling

Callable-Bond Valuation

Callable-Bond Decision Summary

Observed Market Input

Scenario and Interest-Rate Tree Analysis

Additional Call Analysis

Call Option Interest-Rate Scenarios

OAS and Volatility

Interest-Rate Tree

Bond Maturity Ladder

Bond Parameters

Dates

Bond Parameters

Interest Rate Model

Spot Rate and YTM or YTC by Maturity

Prices and Yields by Maturity

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