Is this good for educators?

Yes — this version of "Volatility Surface for a startup valuation" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.

Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Volatility Surface

Volatility Surface for a startup valuation

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a startup valuation live below — adjust the inputs and watch it respond, right in your browser.

Black Scholes

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Black-Scholes Option PricingLive

fair value + the Greeks

Controls

Presets

Spot price S

Strike K

Time to expiry (yr)

Risk-free rate

Volatility σ

The Black-Scholes formula prices a European option from spot, strike, time, rate, and volatility. The Greeks measure sensitivity: delta to price, gamma to delta, vega to volatility, theta to time decay. Educational tool — not investment advice.

▶ Run in Python

Data Inspector

Call price$8.01

Put price$6.03

Delta (call)0.580

Gamma0.0221

Vega (per 1%)0.276

Theta (per day)-0.024

Governing equation

C = S N (d_{1}) - K e^{- r T} N (d_{2}) = 100 \cdot 0.580 - 100 e^{- 0.020} \cdot 0.510 = $8.01

Reading this result: Spot 100 vs strike 100 makes this call at-the-money (intrinsic value 0.00). A higher volatility σ (now 25%) and a longer time to expiry (now 0.50 yr) both raise the option's value by adding time value — more room for the underlying to finish favorably. As the option moves deeper in-the-money its delta approaches 1 and it behaves like the underlying itself.

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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Frequently asked questions

Is this good for educators?: Yes — this version of "Volatility Surface for a startup valuation" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.