Options Pricing Lab.Black-Scholes, decoded.
Estimate the theoretical price of a European call or put from stock price, strike, time, volatility, interest rate, and dividend yield — then see the Greeks and explore how each input moves the number.
Note: Greeks don't predict what will happen — they show how sensitive the model price is to changes in the main inputs.
Compute a theoretical option price
Change any input on the left. Everything on the right updates instantly.
Inputs
Tip: implied volatility is the biggest lever in this model. Try changing IV by ±5% and watch what happens to the theoretical price and vega.
- • This call is currently at the money.
- • About 100% of the current price is time value — mostly a bet on future movement.
- • Delta 0.53 → the option behaves roughly like 53 shares of the underlying.
- • Vega sensitivity: a 1% change in IV moves the price by $0.11 (3.7% of current value).
- • Daily theta: the model loses about $0.05 per day.
Greeks at a glance
Sensitivities of the model priceWhat's driving the current value
Five levers determine every Black-Scholes price. Here's how each one is pulling right now.
Time value dominates — small stock moves matter a lot.
Meaningful time value; theta is moderate.
IV is in a normal range for many stocks.
Higher rates modestly increase call value (cost of carry).
No dividend effect priced in.
Every Greek in plain English
Sensitivities of the theoretical price to a change in one input, with everything else held constant.
How much the option price tends to change when the stock moves by $1.
How fast delta itself changes as the stock moves.
How much time value the model loses per day, all else equal.
How sensitive the price is to a 1% change in implied volatility.
How sensitive the price is to a 1% change in the risk-free rate.
Stress-test the inputs
Move the sliders or click a scenario. This runs alongside your live inputs above.
See how the price bends
A picture of how the theoretical value responds when one input moves and everything else is held constant.
Theoretical price vs. underlying, holding volatility, time, rate, and dividend constant. Dashed line = intrinsic value.
Four scenarios, worked out
Each card runs the same model with different inputs so you can build intuition.
Beginner call
At-the-moneyA one-month ATM call on a $100 stock with typical volatility. Most of the price is time value; delta is near 0.5.
Beginner put
Out-of-the-moneyA short-dated OTM put. Cheap, small delta, and heavily dependent on volatility and remaining time.
Higher volatility
IV 60%Same call, double the vol. Notice how much richer the option becomes — this is what an earnings-week bid looks like.
Near expiration
5 days leftIn-the-money and about to expire. Intrinsic value dominates and theta bleed is severe.
What you're actually looking at
Short, honest explanations — no jargon walls.
What is the Black-Scholes model?
A closed-form pricing formula, published in 1973, that gives a theoretical fair value for a European-style option based on six inputs: stock price, strike, time, volatility, risk-free rate, and dividend yield.
What assumptions does it make?
Log-normal returns with constant volatility, continuous trading with no transaction costs, no arbitrage, a known constant risk-free rate, no early exercise (European style), and continuous dividend yield.
What does 'theoretical value' actually mean?
It's the price the model says the option should trade at given the inputs. Real market prices reflect supply and demand, changing IV, liquidity, and sentiment — so quotes can differ, often meaningfully.
Why do American options differ?
American options can be exercised early. That optionality often makes them worth at least as much as the European price. For non-dividend-paying stocks, American calls tend to match closely; American puts can be worth notably more.
Why does volatility matter so much?
Volatility is the model's estimate of how much the underlying will move. Bigger expected moves = more chance of ending deep in the money = higher option value. Vega isolates that sensitivity.
Common questions
Quick answers to the questions that come up most.
Is this a real market price?
Why is my broker's price different from what this shows?
What does implied volatility do?
Why does theta accelerate near expiration?
Can I use this for American options?
Why can two options with similar strikes have very different prices?
Spreadsheet versions
Prefer to work in Google Sheets? Two companion models — the official Future Ready build and an independent reference — use the same Black-Scholes inputs.
Future Ready Black-Scholes Model
The original Future Ready spreadsheet — mirrors this lab exactly. Open it to edit inputs, inspect the formulas, or copy it into your Drive.
Independent reference model
A separate implementation built by an independent source — useful as a cross-check to verify the same inputs against a different construction.
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