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Call & Put Option Calculator
Price call and put options using the Black-Scholes model. Calculate premium, Greeks (delta, gamma, theta, vega), break-even price, and P/L at expiry.
Option Premium⧉
$3.19
Black-Scholes fair value for this call
Intrinsic Value⧉
$0.00
Value if exercised immediately
Time Value⧉
$3.19
Premium above intrinsic — decays to $0 at expiry
Break-Even Price⧉
$183.19
Stock price needed at expiry to break even
Delta (Δ)⧉
0.3801
Price change per $1 move in stock
Gamma (Γ)⧉
0.0303
Rate of change of delta per $1 stock move
Theta (Θ)⧉
-0.0879
Daily time decay (price lost per day)
Vega (ν)⧉
19.1366
Price change per 1% increase in volatility
Moneyness
OTMATMITM
Profit/Loss at Expiry
| Stock Price | Payoff | P/L per Contract | P/L % |
|---|---|---|---|
| $144.00 | $0.00 | -$3.19 | -100.0% |
| $148.00 | $0.00 | -$3.19 | -100.0% |
| $152.00 | $0.00 | -$3.19 | -100.0% |
| $156.00 | $0.00 | -$3.19 | -100.0% |
| $160.00 | $0.00 | -$3.19 | -100.0% |
| $164.00 | $0.00 | -$3.19 | -100.0% |
| $168.00 | $0.00 | -$3.19 | -100.0% |
| $172.00 | $0.00 | -$3.19 | -100.0% |
| $176.00 | $0.00 | -$3.19 | -100.0% |
| $180.00 | $0.00 | -$3.19 | -100.0% |
| $184.00 | $4.00 | $0.81 | 25.5% |
| $188.00 | $8.00 | $4.81 | 150.9% |
| $192.00 | $12.00 | $8.81 | 276.4% |
| $196.00 | $16.00 | $12.81 | 401.9% |
| $200.00 | $20.00 | $16.81 | 527.4% |
| $204.00 | $24.00 | $20.81 | 652.8% |
| $208.00 | $28.00 | $24.81 | 778.3% |
| $212.00 | $32.00 | $28.81 | 903.8% |
| $216.00 | $36.00 | $32.81 | 1,029.3% |
Planning notes, formulas, and examples
About the Call & Put Option Calculator
Options give you the right — but not the obligation — to buy (call) or sell (put) an underlying asset at a specified price before a certain date. The Black-Scholes model is the foundational framework for pricing European-style options, and it remains widely used across finance.
This calculator prices both call and put options using the Black-Scholes formula, accounting for the underlying price, strike price, time to expiry, volatility, risk-free rate, and dividend yield. It computes the key Greeks — delta, gamma, theta, vega, and rho — which measure the option's sensitivity to various factors.
The profit/loss table shows your potential outcomes at expiry across a range of stock prices, helping you make informed decisions about whether an option trade fits your risk/reward profile. Preset scenarios for common trades let you quickly explore how different setups behave.
When This Page Helps
Use this to estimate a theoretical option premium and see how price, volatility, time, rates, and dividends affect the contract. It also surfaces the Greeks, which are useful for understanding directional exposure and time decay.
How to Use the Inputs
- Select whether you are pricing a call or put option.
- Enter the current stock price (spot price).
- Enter the strike price of the option contract.
- Enter the days until expiration.
- Enter the implied volatility (check your broker's option chain for this value).
- Enter the risk-free interest rate and dividend yield.
- Review the premium, Greeks, break-even price, and P/L table.
Formula used
Call = S₀·e^(-qT)·N(d₁) − K·e^(-rT)·N(d₂)
Put = K·e^(-rT)·N(−d₂) − S₀·e^(-qT)·N(−d₁)
d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T)
d₂ = d₁ − σ√T
Where S = spot, K = strike, T = time, r = risk-free rate, σ = volatility, q = dividend yield.Example Calculation
Result: Premium ≈ $3.25
A call option with strike $180 on a $175 stock with 30 days to expiry and 25% IV is priced around $3.25. The break-even stock price at expiry is $183.25. Delta of ~0.38 means the option gains about $0.38 for every $1 stock increase.
Tips & Best Practices
- Compare your calculated premium to the market price — large differences may indicate overpriced or underpriced options.
- Delta approximates the probability of finishing in-the-money at expiry.
- Theta decay accelerates in the last 30 days — option sellers target this period.
- Use vega to understand the impact of volatility changes, especially around earnings announcements.
- Always check implied vs historical volatility before trading.
How It Helps
The Black-Scholes model provides a standard benchmark for European-style option pricing. This calculator uses the main contract inputs to estimate premium and Greeks, then shows the break-even level and expiry profit or loss across a range of stock prices.
What To Check
Match the expiration format, volatility estimate, and dividend yield to the contract you are pricing. Option values are especially sensitive to implied volatility and time remaining, so use live market inputs when you want a tradeable comparison.
Usefully Interpreted
The output is a theoretical price, not a guaranteed market quote. Actual premiums can differ because of bid-ask spread, early-exercise features, and volatility skew.
Sources & Methodology
Last updated:
Methodology
This worksheet prices a European-style call or put with the Black-Scholes model using the spot price, strike, time to expiry, implied volatility, risk-free rate, and dividend yield shown on the page. The premium is computed from the standard Black-Scholes formula, while delta, gamma, theta, vega, and rho are estimated numerically from small changes in the underlying inputs rather than from closed-form Greek formulas.
The profit-and-loss table is an expiry payoff view built from the model premium, not a path-dependent options simulation. The page is intended as a theoretical benchmark for European-style contracts, so American early-exercise value, bid-ask spread, skew, and liquidity effects are outside the model.
Sources
- What is an Option? (The Options Industry Council) — OIC primer on the structure of calls, puts, strikes, and expiration.
- Options Pricing (The Options Industry Council) — OIC reference on model pricing inputs such as volatility, time, and rates.
- Understanding Options Greeks (The Options Industry Council) — OIC guide to delta, gamma, theta, vega, and rho.
Frequently Asked Questions
Delta measures how much the option price changes for a $1 move in the underlying. A delta of 0.50 means the option gains $0.50 when the stock rises $1.
Theta is time decay — the amount of value the option loses each day. Option sellers benefit from theta; buyers fight against it.
IV is the market's expectation of future volatility priced into the option. Higher IV means more expensive options.
Black-Scholes is designed for European options. American options (which can be exercised early) may be worth slightly more, especially puts.
For calls: strike + premium. For puts: strike − premium. The stock must pass this level at expiry for you to profit.
It provides a solid theoretical baseline, but real option prices deviate because of volatility skew, dividends, liquidity, and early-exercise features. It is most useful as a benchmark, not as a perfect market quote.
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