Do I need to install anything?

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

For Students · Options Desk

Options Desk for a retirement fund

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a retirement fund 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.

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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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Option Payoff

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Option Strategy PayoffLive

profit/loss at expiry

Controls

Presets

Center strike

An option strategy's payoff diagram plots profit or loss against the underlying price at expiration. Combining calls and puts at different strikes shapes the curve — capping risk, capturing volatility, or generating income. Educational tool, not investment advice.

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Data Inspector

Max profit$5.00

Max loss$-5.00

Net debit/credit$5.00

Legs2

Governing equation

Π (S) = i \sum q_{i} [max (S - K_{i}, 0)_{call}, max (K_{i} - S, 0)_{put} - p_{i}], K = 100

Reading this result: Both profit and loss are capped, so this is a defined-risk position — you trade unlimited upside for a known worst case.

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 students?: Yes — this version of "Options Desk for a retirement fund" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.