What this options calculator estimates
This independent Pineify tool models a single plain-vanilla call or put from spot price, strike, time, volatility, risk-free rate and a continuous dividend yield. It does not retrieve Cboe quotes or verify a listed contract. The model premium supplies the entry price for the long-option payoff chart; actual fills, fees and taxes can change the result.
Check the contract before choosing inputs
Exercise style, settlement and multiplier are separate contract terms. Standard equity options commonly represent 100 shares, while SPX uses a $100 multiplier and cash settlement. A numeric multiplier only scales this calculator’s values; selecting 1000 does not turn the spot-based model into a futures-option model. Adjusted deliverables and discrete dividends are not modeled.
Use Cboe’s SPX contract specifications and the exact contract’s broker or exchange documentation. Tick size, last trading time and settlement conventions vary; they are not inferred by this form.
European and American valuation
For European exercise, Black-Scholes uses constant volatility, rates and continuous dividend yield. Let S be spot, K strike, T years, r rate, q dividend yield and σ volatility, with rates expressed as decimals. N is the standard normal cumulative distribution.
d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T); d₂ = d₁ − σ√T
Call = S e−qT N(d₁) − K e−rT N(d₂)
Put = K e−rT N(−d₂) − S e−qT N(−d₁)
The binomial tree compares continuation value with immediate exercise at each node for American options. Selecting Black-Scholes with American exercise resolves to a 200-step tree, including for the Greek calculations. Explicit Binomial Tree uses the selected step count. Results can oscillate as steps change, so increasing steps is a convergence check rather than an accuracy guarantee.
With hypothetical S = K = 100, T = 1 year, r = 5%, q = 0 and σ = 20%, the European call is about 10.4506 and put about 5.5735. Put-call parity gives call − put = 100 − 100e−0.05 ≈ 4.8771. These are model examples, not market quotes.
Use the outputs consistently
- Choose call or put and the contract’s actual exercise style. Enter positive spot and strike, remaining time, contract-specific IV, rate and dividend-yield assumptions.
- Choose the multiplier and whole contract quantity. All inputs must use consistent currency and quote units. The available multipliers are scaling choices, not a product directory.
- Compare the model price with a dated bid/ask quote. P/L and breakeven assume the long option was purchased at model price; they do not use your broker’s execution price.
- Inspect sensitivity and time charts separately. They change one input while holding the rest fixed; they are not a forecast of the price path.
For a hypothetical call bought at 3 with strike 100 and a 100 multiplier, expiry at 110 produces (110 − 100 − 3) × 100 = 700 profit before costs; expiry at or below 100 loses 300. A short uncovered call has unbounded upside-price risk, so the displayed long maximum loss does not apply to a seller.
Margin illustration: uncovered equity options only
The displayed margin uses model premium p and out-of-the-money amount OTM. For calls, OTM = max(K − S, 0); for puts, OTM = max(S − K, 0).
A = p + 0.20S − OTM
B = p + 0.10S (call), or p + 0.10K (put)
Illustrated margin = max(A, B) × multiplier × contracts
At S = 100, K = 105 and p = 3, a one-contract call with multiplier 100 gives max(3 + 20 − 5, 3 + 10) × 100 = 1,800. This is an equity-option illustration, not a universal Cboe minimum. Broad-based index rules use a different percentage, and covered positions, spreads, futures and portfolio margin need other treatment. Broker house requirements may be higher; consult Cboe’s margin guidance and your broker.
Greeks describe local model sensitivity
- Delta and gamma use finite spot-price differences. The displayed values are per underlying unit; multiply by contract size and quantity for position scaling.
- Theta is the modeled change after one day, or the remaining fraction of a day near expiry. It need not be negative in every case.
- Vega and rho are price changes per one percentage point of volatility and interest rate. They do not mean a 1% relative change.
- Leverage is |delta| × S / model price. It omits direction; a put’s delta is generally negative. This local approximation changes as spot and volatility move.
At expiry, price equals intrinsic value and Greeks display N/A. Zero volatility is outside this tool’s accepted input range. Invalid tree probabilities produce an error; increase the step count or review the rate/volatility assumptions instead of relying on a broken estimate.
VIX and dividend assumptions have limits
Cboe describes VIX as a 30-day measure derived across SPX strikes and expirations. It is not the IV of a particular contract and is not an input that makes this calculator suitable for VIX options. Use contract-specific IV for comparison, or label your number as a scenario assumption.
A constant dividend yield cannot represent the timing and amount of a discrete cash dividend. Early exercise, spreads and settlement mechanics can make actual option values and obligations differ from these estimates. This page supports checking assumptions, not selecting profitable trades or executing an automated options strategy.