AI Generated Analytics Dashboard

Yield curve construction, BK 1f pricing, Hull-White tree benchmarks, and practical fixed-income risk workflows.

Dashboard: Live Primary Model: BK 1F Mode: Interactive
Overview Curve Model Pricing Risk

Model Guide

BK 1f first, Hull-White as benchmark

This tab summarizes the two short-rate model families in the app, how their parameters behave, and how to choose between the two tree-based pricing approaches.

Open Curve Open Pricing

Model Inputs

Configure the model method and its matching parameters here first. The Pricing tab reads this saved setup, collects instrument inputs, and focuses on valuation results.

HW1f Parameters

BK1f Parameters

HW1f_Tree pricing is active.
Open Pricing Results

Model Families

BK1f

Black-Karasinski 1-factor is the primary practical stack in this app. It keeps rates positive and supports a calibrated tree for production-style pricing and scenario analysis.

HW1f

Hull-White 1-factor remains available as a lightweight benchmark and teaching model. It is useful for quick comparison and for checking tree behavior on a simpler setup.

Parameter Meaning

Mean Reversion a

Controls how quickly the short rate pulls back toward its fitted level. Larger values make the process revert faster and usually compress the range of future short-rate states.

Sigma

Controls the short-rate volatility. Larger sigma increases the dispersion of future rates and tends to raise option values.

Curve Fit

The initial curve still anchors the pricing setup. BK1f uses a calibrated tree shift, while HW1f uses its own calibrated term-structure fit.

Engine Comparison

Method Main Use Strength Tradeoff
BK1f_Tree Primary production-style pricing Exact curve fit, strong callable / Bermudan support Discrete lattice method
HW1f_Tree Benchmark lattice pricing Fast and simple sanity-check model Less practical than BK for the main app focus

Sample Tree

Six displayed layers from the root to a 2.5Y horizon. Node labels show short rate r and state price q on a calibrated BK tree.

t=0.0y t=0.5y t=1.0y t=1.5y t=2.0y t=2.5y r=4.40% q=1.0000 r=4.54% q=0.1630 r=4.59% q=0.6522 r=4.65% q=0.1630 r=4.53% q=0.0229 r=4.58% q=0.2121 r=4.64% q=0.4862 r=4.70% q=0.2120 r=4.76% q=0.0229 r=4.57% q=0.0027 r=4.62% q=0.0444 r=4.68% q=0.2218 r=4.74% q=0.3963 r=4.79% q=0.2217 r=4.85% q=0.0444 r=4.91% q=0.0027 r=4.60% q=0.0003 r=4.66% q=0.0071 r=4.71% q=0.0603 r=4.77% q=0.2180 r=4.83% q=0.3413 r=4.89% q=0.2178 r=4.95% q=0.0602 r=5.01% q=0.0070 r=5.07% q=0.0003 r=4.63% q=0.0000 r=4.69% q=0.0009 r=4.75% q=0.0117 r=4.81% q=0.0710 r=4.87% q=0.2099 r=4.93% q=0.3039 r=4.99% q=0.2096 r=5.05% q=0.0708 r=5.11% q=0.0117 r=5.17% q=0.0009 r=5.24% q=0.0000

Workflow Guidance

  1. Build or edit the curve on the Curve tab first.
  2. Use the Model tab to understand BK 1f versus Hull-White, choose the model family you want, and set model parameters.
  3. Go to the Pricing tab to enter instrument inputs and run valuations.
  4. Use the Pricing results to compare bonds, options, callable structures, and swaptions.
  5. Finish on the Risk tab for shocked comparisons and portfolio-style analysis.

Notes

The BK PDE components remain in the repository for diagnostics and numerical research, but the main live workflow currently centers on the BK tree.

The live site is intentionally streamlined around tree-based analytics so the workflow stays fast and predictable on compact deployments.