Choose call or put
Select a call when the modeled right is to buy at the strike, or a put when the modeled right is to sell at the strike. The calculator changes the pricing and Greek equations automatically.
MODEL-BASED OPTIONS PRICING
Option Price Calculator
Estimate a call or put's theoretical price from stock price, strike, time remaining, volatility, interest rate, and dividend yield. The result is a model estimate, not a live quote.
- Runs in your browser
- Call and put models
- Shows the assumptions
A pricing model, not a prediction
Use the number to understand how assumptions affect value. Compare it with a current bid, ask, and contract specification before making a trade.
WORKING CALCULATOR
Calculate a theoretical option price
Start with the example or enter your own scenario. Percentages are annual rates, and the contract multiplier is normally 100 shares.
01
INPUTS
Describe the option
02
RESULT
Estimated option value
Example result
Model estimate
With a $100 stock price, a $105 strike, 60 days remaining, and 25% volatility, the example call is estimated at $2.35 per share.
Theoretical value
$2.35
Call theoretical value per share
Position value
$235.34
Intrinsic value$0.00
Time value$2.35
d1-0.358
d2-0.459
SENSITIVITIESPer share unless noted
| Metric | Value | What it describes |
|---|---|---|
| Delta | 0.360 | Approximate price change for a $1 underlying move. |
| Gamma | 0.037 | How delta changes as the underlying moves. |
| Theta / day | -$0.04 | Approximate daily time decay with other inputs fixed. |
| Vega / 1% | $0.15 | Approximate value change for a one-point volatility move. |
| Rho / 1% | $0.06 | Approximate value change for a one-point rate move. |
Model used
Call value = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)
The displayed value is an estimate under the selected assumptions. It is not a tradable bid, ask, or guarantee.
HOW IT WORKS
How to use the option price calculator
A useful result depends on consistent assumptions. Complete the fields in order, then read price and sensitivities together instead of treating one number as a forecast.
Enter market terms
Add the current or assumed underlying price and strike. These two values determine whether the option is currently in, at, or out of the money.
Add time and volatility
Enter calendar days remaining and annualized implied volatility. More time or volatility often increases extrinsic value, but the exact effect depends on the other inputs.
Read the result
Review theoretical value per share, position value, intrinsic value, time value, and the sensitivity table. Change one assumption at a time when comparing scenarios.
INPUT GUIDE
What each input means
The Black-Scholes-Merton model is only as useful as its assumptions. These fields explain what to enter and which shortcuts can make a result look too precise.
Underlying and strike
Use the same price unit for the stock and strike. A call is generally more valuable when the underlying rises above the strike; a put is generally more valuable when it falls below the strike. The calculator does not retrieve or verify a ticker quote.
Time to expiration
The tool converts days to expiration into years using 365 days. Enter the remaining calendar time you want to model, not the number of trading sessions. A short-dated option can be highly sensitive to a small change in this input.
Implied volatility
Enter volatility as a percentage, such as 25 for 25%, not 0.25. Volatility is an expectation of movement, not a direction. A higher value normally raises the time value of both calls and puts in this model.
Rates and dividends
The interest rate and dividend yield are annual assumptions. Use a rate that matches the currency and date of the scenario. If a stock has no modeled dividend, enter zero; do not insert a cash dividend amount into a yield field.
Contracts and multiplier
The per-share estimate is multiplied by contracts and the contract multiplier to show a position value. Standard equity options commonly use 100 shares, but adjusted contracts and other products can differ, so verify the contract specification.
READ THE OUTPUT
What the calculator shows
The result panel separates value from sensitivity, helping distinguish the model's estimate from what a real position could gain or lose as conditions change.
Theoretical value
This is the model's estimated premium per share. Position value multiplies it by the contract count and multiplier. It is not a recommendation, a guaranteed fill price, or a statement that the market must trade there.
Intrinsic and time value
Intrinsic value is the immediate exercise value at the selected underlying price. The remaining model price is time value. An out-of-the-money option has zero intrinsic value but can still have time value.
Greeks
Delta, gamma, theta, vega, and rho describe local sensitivity to selected inputs. They are approximations around the current scenario, not fixed promises over the life of the option.
d1 and d2
The intermediate d1 and d2 values are shown so advanced users can audit the model path. They are inputs to the normal-distribution terms used by the Black-Scholes-Merton equations.
METHOD
How the pricing model works
This page uses the European-style Black-Scholes-Merton framework for learning and scenario analysis. Real markets also include exercise style, liquidity, skew, discrete dividends, and supply and demand.
Annualize the clock
Days remaining are divided by 365 to create T, the time in years. The stock price, strike, rate, dividend yield, and volatility are then combined over that time interval.
T = days to expiration ÷ 365Build d1 and d2
The model compares the log relationship between spot and strike with the carry and volatility assumptions. d2 is d1 adjusted by one volatility-time interval.
d1 = [ln(S/K) + (r − q + σ²/2)T] ÷ (σ√T); d2 = d1 − σ√TDiscount the two legs
A call combines the discounted expected stock benefit and strike payment. A put uses the corresponding downside terms. The normal cumulative distribution N(·) supplies the probability weights in the model.
Call = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)Derive the Greeks
The calculator derives local delta, gamma, theta per day, vega per one volatility point, and rho per one rate point from the same d1 and d2 values. Units are stated beside each result.
Put = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1)LIMITS AND CARE
Why a model price can differ from the market
A theoretical value is a calculation, not a live market measurement. Check the following before comparing it with a broker screen or using it in a trade decision.
European-style assumption
The basic equations model a European exercise profile. American-style equity options can be exercised before expiration, especially around dividends, so the result may not match a full early-exercise model.
Volatility is not constant
The calculator uses one volatility number for the whole scenario. Real option chains can show volatility skew and term structure, while a single input smooths those differences away.
Quotes include the market
Bid-ask spreads, liquidity, order size, fees, assignment, and stale quotes all affect a trade. The model has no account, exchange, quote feed, tax treatment, or execution context.
Edge cases need judgment
A zero or missing volatility, zero days, invalid rates, or a wrong multiplier can make a result meaningless. The form blocks invalid ranges, but it cannot decide whether your assumption is economically sensible.
LEARN MORE
Use an educational reference too
For broader explanations of option pricing, Greeks, exercise style, and investor disclosures, consult the Options Industry Council.
RELATED TOOL
Continue with the right model
Separate calculators keep each option question and its assumptions clear. Choose the tool that matches your question.
Options Profit Calculator
Need expiration profit, loss, breakeven, or payoff scenarios instead of a theoretical option premium? Return to the homepage calculator for strategy-based P/L.
Probability and implied volatility are different questions
A probability estimate asks about the chance of a price event, while implied volatility solves for the volatility that best matches an observed premium. They should not be inferred from this page's price alone.
FAQ
Option price calculator FAQ
These questions cover the most common interpretation and input mistakes when using a theoretical option pricing model.
What is an option price calculator?
It is a tool that estimates a call or put's theoretical premium from inputs such as the underlying price, strike, time, volatility, interest rate, and dividend yield. This page uses the Black-Scholes-Merton framework and labels the result as an estimate.
How is an option price calculated?
The model converts days into years, calculates d1 and d2, applies discounted stock and strike terms, and uses the normal distribution to produce a call or put value. The exact result changes when any assumption changes.
Should volatility be entered as 25 or 0.25?
Enter 25 when the field is labeled as a percentage. The calculator converts that input to 0.25 internally. Entering 0.25 would mean 0.25%, which is a very different assumption.
Why does the calculator price differ from my broker?
A broker quote reflects market supply and demand, bid-ask spread, exercise style, volatility surface, discrete dividends, interest assumptions, fees, and timing. This calculator uses a simplified single-volatility model and no live quote feed.
What do the Greeks mean in the result?
Delta estimates sensitivity to a $1 underlying move; gamma describes how delta changes; theta shows approximate daily time decay; vega uses a one-point volatility move; and rho uses a one-point rate move. They are local estimates, not guarantees.
Can I use this option price calculator for a real trade?
You can use it for education and scenario comparison, but verify the contract, quote, expiration, volatility, dividends, fees, and exercise terms independently. The page does not recommend trades or assess whether a position is suitable for you.
NEXT STEP
Change one assumption and compare again
A small scenario table is often more useful than a single output. Try a different volatility or expiration, then compare the result with a real option chain and its timestamp.