A call's model value comes from five inputs: share price, strike, time to expiry, volatility and an interest rate. The calculator runs them through the Black-Scholes formula and gives a value per share.
Treat it as a fair-value benchmark, not a quote you can trade at. Here's what each input does, how to read the result, and where the model stops matching real options.
What a call gives you, and what it costs
A call gives you the right to buy a stock at a set price, the strike, for a set period. That's how the SEC's investor bulletin on options defines it. The price of the right is the premium.
Premiums are quoted per share, and "an option contract generally represents 100 shares of the underlying stock," the SEC says. At the defaults, the model's $10.45 a share means about $1,045 per contract.
As a buyer, the premium is all you can lose. In FINRA's words, "for the purchaser of an option, the premium paid is your maximum loss."
The formula behind the number
S is the share price, K the strike, T the years left, σ the volatility and r the rate. N( ) turns a number into a probability from the normal curve.
The calculator also shows d₁ and d₂, the formula's middle steps. N(d₁) is the call's delta, the change in value per $1 move in the share. At the defaults, d₁ is 0.35, so the delta is about 0.64.
You can test it. Raise the share price from $100 to $101 and the value goes from $10.45 to $11.10, a 65-cent gain. The same inputs also price the matching put, the right to sell: $5.57 at the defaults.
Intrinsic value and time value
FINRA defines intrinsic value as an option's value "if it were to expire immediately." Time value, in FINRA's terms, is the part of the premium attributable to the time remaining.
For a call, intrinsic value is the share price minus the strike, when that's positive. The SEC calls such a call in-the-money: the strike is below the stock price. Here's a $100 share with three months to run, 20% volatility and a 5% rate:
| Strike | Where it stands | Call value |
|---|---|---|
| $80 | In the money | $21.02 |
| $90 | In the money | $11.67 |
| $100 | At the money | $4.61 |
| $110 | Out of the money | $1.19 |
| $120 | Out of the money | $0.20 |
At a $90 strike, $10 of the $11.67 is intrinsic and $1.67 is time value. At $100 the whole $4.61 is time value, and it's the largest in the table. Time value shrinks as the strike moves away in either direction.
Where does a buyer break even?
At expiry, only intrinsic value is left. So a buyer breaks even when the share price equals the strike plus the premium paid.
Buy the three-month $100 call at its model value of $4.61, and the share must reach $104.61 by expiry. That's a 4.6% rise just to get your money back. One contract would cost about $461.
The $110 call looks cheaper at $1.19, but it breaks even at $111.19, an 11.2% rise. If the share ends at or below the strike, the call expires worthless. For an option that expires out-of-the-money, the SEC says "the entire premium will be lost."
Which volatility should you enter?
FINRA defines volatility as "a measurement of the fluctuation in the market price of the underlying security." The SEC lists it among the factors that determine a premium, with the share price, strike and time left.
It's the one input that's an estimate of the future. Enter it as an annual percentage. Here's the same three-month, $100-strike call at four volatilities:
| Volatility | Call value |
|---|---|
| 10% | $2.66 |
| 20% | $4.61 |
| 30% | $6.58 |
| 40% | $8.55 |
Each 10 points of volatility adds close to $2 here. The rate matters far less: moving it from 0% to 5% lifts the value from $3.99 to $4.61.
You can estimate volatility from the share's past price swings. Or work backwards from a real quote: change the volatility until the value matches the premium your broker shows. The figure that fits is the market's implied volatility.
Time drains the value, faster near the end
FINRA describes time decay as the way an option's theoretical value "erodes" or reduces as time passes. Enter time in years: one month is 1 ÷ 12, about 0.083. The erosion isn't even, as this at-the-money call shows:
| Time to expiry | Call value |
|---|---|
| 12 months | $10.45 |
| 6 months | $6.89 |
| 3 months | $4.61 |
| 1 month | $2.51 |
| 1 week | $1.15 |
From 12 months to 6, the call loses $3.56, about 2 cents a day. From one month to one week, it loses $1.36 in about three weeks, near 6 cents a day.
In the last week, the remaining $1.15 disappears, about 16 cents a day. All of this assumes the share stays at $100. The final weeks cost a buyer the most per day.
Where Black-Scholes and real options part ways
The formula prices a European-style option. FINRA says such a contract "may only be exercised during a period of time on its expiration date." An American-style one can be exercised any time before expiry.
That gap matters for stocks. In U.S. markets, options on stocks and ETFs are American-style, according to FINRA. FINRA also notes that holders of in-the-money positions might exercise early to benefit from a dividend payout.
The calculator has no dividend input, so it ignores both the payout and that early-exercise right. It also holds volatility fixed for the option's whole life. In practice volatility shifts, so run a few values rather than trusting one.
Buying a call versus selling one
The two sides carry very different risks. A buyer's loss stops at the premium. Sell a call without owning the stock, and FINRA says "the maximum loss is theoretically unlimited."
The SEC's bulletin adds that with options "it is possible to lose all of your initial investment, and sometimes more." According to FINRA, brokerage firms are required to distribute Characteristics and Risks of Standardized Options to options customers.
A spread limits both sides: buy one call and sell another at a higher strike. The options spread calculator shows its maximum profit, maximum loss and break-even. Futures carry leverage too, with no premium and no cap on losses. The futures contracts calculator shows a position's full size.