How do I simulate a yield curve?

Open this page and use the live Portfolio Builder tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a yield curve from your own measurements.

Use case · powered by Portfolio Builder

Portfolio Builder for a yield curve

Simulate a yield curve live in your browser. This runs the real Portfolio Builder solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Efficient Frontier

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Efficient FrontierLive

Markowitz portfolio theory

Controls

Presets

Asset A return

Asset A volatility

Asset B return

Asset B volatility

Correlation

Combining two assets traces a curved frontier of risk versus return. Because they are not perfectly correlated, some mixes have lower risk than either asset alone — the power of diversification. The pink point is the minimum-variance portfolio. Educational tool, not investment advice.

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Data Inspector

Min-var weight A0%

Min-var return0.0%

Min-var volatility0.0%

Governing equation

σ_{p}^{2} = w^{2} σ_{A}^{2} + (1 - w)^{2} σ_{B}^{2} + 2 w (1 - w) ρ σ_{A} σ_{B}, ρ = 0.20, w^{*} = 0%

Reading this result: The assets differ sharply in volatility, so the minimum-variance blend leans heavily toward the calmer one to hold total risk down.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Monte Carlo

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Monte Carlo Price SimulationLive

geometric Brownian motion

Controls

Presets

Initial price S₀

Expected return μ

Volatility σ

Horizon (years)

Geometric Brownian motion models a price with constant drift and random volatility — the assumption behind Black-Scholes. Running hundreds of simulated paths reveals the full distribution of outcomes, not just an average. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

Median outcome$0

5th percentile$0

95th percentile$0

Governing equation

S_{t + Δ t} = S_{t} e^{(0.07 - \frac{0. 2 ^{2}}{2}) Δ t + 0.2 Δ t Z}, \tilde{S}_{1} \approx $0

Reading this result: Median outcome is about $0, just under the drift-only $107 — GBM compounds in log-space, so volatility always pulls the typical path below the average.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Value At Risk

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Value at Risk (VaR)Live

parametric VaR & expected shortfall

Controls

Presets

Portfolio value ($)

Annual volatility

Annual return

Horizon (days)

Value at Risk estimates the loss a portfolio will not exceed over a horizon at a confidence level. Parametric VaR assumes normally distributed returns and scales volatility by √time. Expected shortfall (CVaR) is the average loss in the tail beyond VaR. Educational tool, not investment advice.

▶ Run in Python

Data Inspector

VaR (95%)$20,446

Expected shortfall$25,708

Horizon vol1.26%

Governing equation

VaR_{95%} = z σ - μ = 1.64 \times 0.0126 - 0.0003 = 0.0204

Reading this result: At 95% confidence the loss should not exceed 2.0% of the portfolio over 1 day; the average loss in the worse tail beyond that (expected shortfall) is steeper still.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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About this simulation

The full Portfolio Builder tool models a yield curve with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

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Other ways to simulate a yield curve

Black-Scholes for a yield curve Option Payoff for a yield curve Monte Carlo (GBM) for a yield curve Efficient Frontier for a yield curve Value at Risk for a yield curve Bond Pricing for a yield curve

Frequently asked questions

How do I simulate a yield curve?: Open this page and use the live Portfolio Builder tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a yield curve from your own measurements.