Option pricing calculator
Price a call or put with Black-Scholes-Merton, see d1, d2, N(d1), N(d2) and the Greeks, and derive the dividend yield and implied volatility that reproduce an actual premium.
Overview
The Option pricing calculator is a Black-Scholes worksheet. You type the stock price, strike, days to expiration, implied volatility, risk-free rate and dividend yield; it returns the theoretical call and put price, the intermediate terms d1, d2, N(d1) and N(d2), and the Greeks for the option type you chose. If you also type the premium the option actually trades at, it works backwards to the dividend yield and the implied volatility that would produce that premium.
Use it to understand what drives an option's value, to sanity-check a premium you see in the Options screener, or to see how much theta or vega a contract carries.
The calculator uses only the numbers you enter; when you copy them from a screen, that data's delay depends on your plan and is shown on every view. The output is a theoretical model value, an estimate, and the page says so ("Model output, not a quote").
Before you start
- Any signed-in user can use the calculator; no Pro plan is needed.
- Have the inputs ready: the underlying price, the strike, the calendar days left to expiration and an implied volatility. The Metric glossary explains implied volatility and the Greeks.
Steps
- Open Research → Tools and click Option pricing calculator. The form opens filled with a sample worksheet (the same one the Load TRIP example button reloads).
- Choose Option type: Call or Put. This sets which Greeks are shown and which price the actual-premium solver targets.
- Fill Stock price (S), Strike price (X), Days to expiration and Implied volatility %.
- Adjust Risk-free rate % and Dividend yield % if needed (after Clear they reset to
4.5and0). - Optional: type the market premium in Actual premium (optional).
- Press Calculate. Clear empties the form and the output.
Percent boxes take percent: type 32 for 32 %, not 0.32.
Inputs and outputs
| Input | Meaning |
|---|---|
| Option type | Call or put. Both prices are always shown; the Greeks and the solver follow this choice. |
| Stock price (S) | Underlying price. Must be above 0. |
| Strike price (X) | Exercise price. Must be above 0. |
| Days to expiration | Calendar days (decimals allowed). Converted to years as T = days / 365. |
| Implied volatility % | Annualised volatility, in percent. |
| Risk-free rate % | Annual continuously compounded rate, in percent. |
| Dividend yield % | Continuous dividend yield, in percent. |
| Actual premium (optional) | The observed price per share. Leave blank to skip the solver. |
| Output | What it means / formula |
|---|---|
| T (years) | days / 365. |
| d1 | [ln(S e^(-qT) / X) + (r + sigma^2 / 2) T] / (sigma sqrt(T)), where q is the dividend yield, r the rate and sigma the IV. |
| d2 | d1 - sigma sqrt(T). |
| N(d1), N(d2) | Standard normal cumulative probability of d1 and d2. N(d1) equals the call delta when the dividend yield is 0; N(d2) is the model's risk-neutral probability that a call finishes in the money. |
| Call price | S e^(-qT) N(d1) - X e^(-rT) N(d2). |
| Put price | X e^(-rT) N(-d2) - S e^(-qT) N(-d1). |
| Delta | Change in option price per $1 move in the stock. |
| Gamma | Change in delta per $1 move in the stock. |
| Theta (per day) | Change in option price per calendar day that passes (usually negative for a long option). |
| Vega (per vol point) | Change in option price for a 1-point (1 %) rise in implied volatility. |
| Rho (per 1 %) | Change in option price for a 1 % rise in the risk-free rate. |
| Derived dividend yield | The dividend yield (searched between -100 % and +100 %) that makes the model price equal the actual premium, keeping your IV. Shows not reachable when no yield in that range does. |
| Implied volatility | The volatility that makes the model price equal the actual premium, at the dividend yield you entered. not reachable when no volatility can (for example a premium below intrinsic value). |
| Calculation variance | Model price minus actual premium, at the inputs as entered. Positive means the model price is higher than the market premium. |
The note under the output names the model: Black-Scholes-Merton with a continuous dividend yield. The worksheet the tool is based on also listed a tax rate, but its formula never used one, so there is no tax input.
How to read it
- Moneyness through d1 and d2. Negative d1 and d2 with a call mean the strike is above the forward price (out of the money); the further below zero, the lower N(d2).
- Greeks are per share. Multiply by 100 for one standard contract.
- Calculation variance is the quickest consistency check: close to zero means your IV input is in line with the premium; a large positive value means the IV you typed is higher than the one the market premium implies.
- Put-call parity. Call price minus put price should equal S e^(-qT) - X e^(-rT). If you change only the option type, both prices stay the same.
- When Days to expiration or Implied volatility % is 0, d1 and d2 are undefined and show
—.
Example
Illustrative inputs for the invented symbol XYZ: Call, stock price 50, strike 52, 30 days, implied volatility 40 %, risk-free rate 4.5 %, dividend yield 0 %.
| Output | Value |
|---|---|
| T (years) | 0.082192 |
| d1 | -0.2524 |
| d2 | -0.3671 |
| N(d1) | 0.4004 |
| N(d2) | 0.3568 |
| Call price | $1.5342 |
| Put price | $3.3422 |
| Delta | 0.4004 |
| Gamma | 0.0674 |
| Theta (per day) | -0.0392 |
| Vega (per vol point) | 0.0554 |
| Rho (per 1 %) | 0.0152 |
Reading it: the model values the call at about $1.53 per share ($153 per contract). One more day passing costs about $0.039 per share, and one more point of implied volatility adds about $0.055. Parity check: 1.5342 - 3.3422 = -1.8080, which equals 50 - 52 e^(-0.045 x 0.082192). The figures are illustrative only.
Using it in your research
- How much of this premium is time value, and how quickly does theta erode it as expiration approaches? Re-run with fewer days.
- How sensitive is the price to a change in implied volatility, for example around an earnings date? Re-run with a higher and a lower IV.
- Is the premium shown in the screener consistent with its listed IV? Enter it as the actual premium and look at Calculation variance and the solved Implied volatility.
- Does the market premium imply a different dividend expectation than you assumed? Check the Derived dividend yield.
FAQs
Does the calculator fetch prices for me?
No. It works only on the numbers you type. Copy the underlying price and IV from a screen, keeping in mind their delay.
Why calendar days and not trading days?
The worksheet the tool reproduces uses calendar days / 365, the same convention as the strategy builder heat map, so the two tools agree.
Is this the price of an American option?
No. Black-Scholes-Merton prices European exercise. For most calls on stocks without large dividends the difference is small, but early exercise value is not modelled.
Troubleshooting
"Please enter the stock price" (or strike, days, implied volatility)
The field is empty, not a number, or out of range. Stock price and strike must be above 0, days and IV cannot be negative. Thousands separators and a trailing % are accepted.
"Enter a premium above 0 or leave blank"
The actual premium box holds 0, a negative number or text. Clear it to skip the solver.
Derived dividend yield or implied volatility says "not reachable"
No value in the search range reproduces the premium you typed. Common causes: the premium is below the option's intrinsic value, or the days or IV inputs are 0.
The implied volatility looks 100 times too small or too large
Percent boxes take percent. Type 40 for 40 %, not 0.40.