Options Calculator
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Calculator Methodology

The calculator first prices each option at entry, then revalues the position across the chosen prices or dates. All opening premiums are theoretical values calculated from the scenario inputs.

Entry baseline and graph views

Entry price is the underlying price at today’s date used to calculate the leg premiums. Changing it, the contracts, implied volatility, interest rate or dividend yield recalculates the entry values. Analysis date changes the stock-price curve without changing the displayed model prices or Greeks. The time-view price slider edits the same Entry price as the top field, recalculating the opening premiums and position summary.

Expiration value and profit or loss

For final underlying price STS_T and strike KK, expiration values per share are:

Call value=max⁡(ST−K,0),Put value=max⁡(K−ST,0)\text{Call value}=\max(S_T-K,0),\qquad \text{Put value}=\max(K-S_T,0)

A purchased leg contributes positive value and a short leg negative value, scaled by quantity and the 100-share multiplier. The same signs are used for the initial premiums:

P/L=signed position value−signed entry value\text{P/L}=\text{signed position value}-\text{signed entry value}

Between strikes, expiration P/L is linear. Break-evens are found by solving those segments within their valid, nonnegative price ranges. Finite extrema are checked at zero and the strikes; net call exposure determines whether the upper tail is flat or unbounded. When P/L is zero over an interval, the summary shows that price range.

Values before expiration

European-style reference values use the dividend-adjusted Black–Scholes–Merton formula. American options are valued with a strike-centered Leisen–Reimer binomial tree, with a drift-adjusted Cox–Ross–Rubinstein construction used for numerical fallback. Working backward from expiration, the tree compares immediate exercise with the discounted continuation value at each step.

A non-dividend-paying American call uses the European result because early exercise adds no value under the model assumptions and nonnegative rates. Other American values include the early-exercise choice. The continuous dividend yield, annualized volatility and continuously compounded interest rate remain fixed across a curve.

Tree valuations and Greeks are smoothed to reduce changes caused by the finite time steps. Time-view curves interpolate sampled early-exercise premiums and apply value bounds. These numerical approximations are most consequential at short maturities or extreme inputs.

Graph views

Position shows the signed value of the open legs. Profit / loss subtracts their signed entry value. Since this baseline is constant across a curve, subtracting two points gives the same dollar change in either view.

The comparison percentage uses the first displayed amount’s magnitude:

Percentage change=100y2−y1∣y1∣\text{Percentage change}=100\frac{y_2-y_1}{|y_1|}

Here y1y_1 and y2y_2 are the selected P/L or position-value amounts. A change from -$500 to -$200 is therefore +$300 and +60%. A starting magnitude below $0.005 is treated as zero: no displayed change shows 0.00%, and other moves show N/A. Nonfinite results also show N/A. It measures change relative to that plotted amount rather than return on the entry premium or account capital.

Greeks

Summary Greeks use today’s date and the entry underlying price, adding option sensitivities for long legs and subtracting them for short legs after quantity and multiplier scaling. Delta measures value change per $1 underlying move; Gamma measures the change in Delta per $1 move. Theta is per calendar day, and Vega and Rho are per one-percentage-point change in volatility and interest rate. European sensitivities use the formula’s derivatives; American sensitivities use numerical changes in model inputs.

Inputs, rounding, and scope

The calculator supports up to ten call or put legs, whole-contract quantities from 1 to 99, one underlying and one shared American-style expiration. The ticker is a scenario label. Stock legs, adjusted contracts, different-expiration combinations, live quotes and account margin are outside the modeled position.

Dates use whole-day differences divided by 365.25 for valuation; daily Theta uses a 365-day conversion. Same-day expiration has zero model time, so its entry value is intrinsic value. Weekday expirations can be selected up to 39 calendar months ahead; date selection does not check an exchange’s listing or holiday calendar.

Calculations retain more precision than displayed prices. Graphs in strategy articles use their stated premiums and expiration payoffs. Opening an article example transfers its scenario, after which the calculator recomputes entry premiums at the current inputs and date. Trading costs, financing charges, taxes and shares created by assignment are excluded from the results.

Sources

Contracts and trading

Pricing

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