Pineify logo
Instant Risk Analysis

Free Option Risk Calculator

Model one long or uncovered short call or put: expiration payoff, position Greeks, risk-neutral profit probability and a delta-normal VaR approximation. Enter your assumptions; no market data is fetched.

VaR Analysis
All 5 Greeks
100% Free
%
%
%

100 shares total

Total: $350.00

Moneyness
Call:OTM(Out of the Money)
Theoretical: $1.1895Intrinsic: $0.00
Long Call — Risk Summary
Max Loss
$350.00
Max Profit
Unlimited
Breakeven
$108.50
Reward/Risk
∞
Model P(Profit)
13.2%
Risk-Neutral Expected P/L
$-230.56

Value at Risk & Position Details

One Trading-Day Delta-Normal VaR
95% VaR
$72.13
Normal-model 5% upper-loss tail; not a loss limit
99% VaR
$101.99
Normal-model 1% upper-loss tail; not a loss limit
Position Details
Total Premium$350.00
Contracts1 (100 shares)
Intrinsic Value$0.00
Extrinsic Value$1.19
Time to Expiry0.0822 years
Theoretical Price$1.1895
Probability of Profit
0%13.2%100%
European Black-Scholes-Merton assumptions: constant annual volatility, continuous rates/dividend yield and 100 shares per contract. Days use 365/year; VaR uses 252 trading days and delta only, ignoring gamma, jumps and volatility changes. It can exceed a long option’s premium. Probability and expected P/L are risk-neutral model values, not forecasts or investment edge. Fees, early exercise and assignment are not modeled; payoff assumes settlement at expiration.

Single-Leg Option Risk: Payoff and Model Sensitivities

Enter one call or put, long or uncovered short, with a premium quoted per share and a fixed 100-share contract multiplier. The payoff uses that premium; theoretical price and Greeks use the separately entered Black-Scholes-Merton assumptions. Those two prices need not match.

Expiration Payoff

A long call has premium-limited loss and unbounded upside. A long put has premium-limited loss and its best payoff occurs when the underlying reaches zero. Short positions reverse these cash flows: an uncovered short call has unbounded loss, while a short put’s loss is bounded by strike less premium, times the share multiplier. These figures exclude fees and obligations that may arise from exercise or assignment.

Call breakeven is strike plus premium; put breakeven is strike minus premium. A put premium above its strike produces no nonnegative breakeven. The displayed maximum profit or loss is floored at zero when no positive profit or loss exists under the entered payoff.

What the Model Assumes

The pricing and Greeks model is European, with constant annual volatility, continuously compounded rate and continuous dividend yield. Days use 365 per year and months use 12. It does not model American early exercise, discrete dividends, spreads, liquidity, fees or changing volatility. Standard 100-share contracts are assumed; adjusted contracts require a different multiplier.

Probability and Expected P/L

Model probability of profit evaluates the risk-neutral log-normal terminal price distribution at the expiration breakeven. It is not a historical win rate or a real-world success probability. Expected P/L is undiscounted risk-neutral expected terminal payoff minus the entered premium, with the sign reversed for a short position. Financing the premium is excluded.

Why VaR Is Not a Maximum Loss

The one-trading-day delta-normal approximation is z × absolute position delta × spot × volatility / √252. The 95% and 99% figures use z values 1.645 and 2.326. This local linear approximation ignores gamma, volatility shocks and jumps. It can exceed a long option’s premium and does not replace the expiration maximum-loss calculation.

Read Greeks in Position Units

Greeks include the position direction and contracts × 100. Delta measures value sensitivity to a one-dollar spot change; gamma measures change in delta. Theta is value change per calendar day with other inputs fixed. Vega and rho are value changes per percentage-point change in annual volatility and rate. They are local derivatives, not guaranteed future P/L.

Compare Scenarios

  1. Check the premium and contract multiplier against the instrument.
  2. Change spot, volatility or time separately and compare theoretical value and Greeks.
  3. Use the payoff tab to inspect expiration outcomes across the displayed price range. The line chart is not a full distribution or a limit on possible prices.
  4. Evaluate funding, execution and assignment separately before using any result in a trading decision.

Sources

Frequently Asked Questions

Model assumptions, units and limits.

    • What positions does this calculator cover?

      One long or uncovered short call or put, with 100 shares per contract. It does not combine stock hedges or other option legs. Payoff is evaluated at expiration before fees; exercise, assignment and broker margin are not modeled.

    • Are the probability and expected P/L forecasts?

      No. They use a log-normal risk-neutral distribution with drift equal to risk-free rate minus continuous dividend yield. Expected P/L is the undiscounted expected expiration payoff less the entered premium, signed for long or short. It omits financing of the premium and is not a forecast of real-world returns.

    • What does delta-normal VaR mean here?

      The approximation is z × absolute position delta × spot × annual volatility / square root of 252, using z=1.645 or 2.326. It assumes normally distributed one-day changes and constant delta. It omits gamma, jumps and volatility changes, is not a worst-case limit, and may exceed a long option’s premium.

    • How are Greeks scaled?

      Each per-share Greek is multiplied by contracts × 100 and reversed for a short position. Delta is position value sensitivity per one-dollar spot move, gamma is delta change per one-dollar spot move, theta is per calendar day, and vega/rho are per percentage point of annual volatility/rate.

    • What does reward/risk measure?

      Maximum potential profit divided by maximum potential loss at expiration. Unlimited call outcomes lead to an infinite or zero ratio in this simplified convention; this is not a ranking of trade quality. A zero maximum-profit figure means the entered payoff has no positive outcome.

    • What happens at zero time or volatility?

      This implementation requires positive time, volatility, spot and strike, positive whole contracts and nonnegative premium. It does not approximate expiry by a tiny remaining time or calculate zero-volatility limits. Invalid or numerically unrepresentable inputs clear the results.

    • What are the breakeven and payoff limits?

      Call breakeven is strike plus premium; put breakeven is strike minus premium, before fees. If the put result is negative, there is no nonnegative underlying price that breaks even. The chart shows a finite range; it does not cap the unlimited call outcome.

    • Is this calculator free?

      Yes. The arithmetic runs locally without sign-up. It uses manually supplied inputs and makes no claim that its theoretical value is an executable quote.

Explore Pineify’s Coding Assistant

Draft and review TradingView indicators and strategies with Pineify. This calculator does not send orders or turn model probabilities into validated trading signals.

Explore the Coding AgentExplore AI Stock Picker