Options Formula Reference
The formulas you actually need, grouped and ready to use. Payoff, breakeven, spreads, the Greeks, and risk maths — each links to a fuller explanation.
Options Formula Reference: This reference collects the essential options formulas — payoff and breakeven, intrinsic and time value, spread and Iron Condor maths, the Black-Scholes Greeks, and position-sizing and expected-value formulas — in one place.
Payoff & breakeven
| Long call payoff | max(S − K, 0) − premium |
|---|---|
| Long put payoff | max(K − S, 0) − premium |
| Call breakeven | Strike + premium paid |
| Put breakeven | Strike − premium paid |
| Intrinsic value (call) | max(S − K, 0) |
| Intrinsic value (put) | max(K − S, 0) |
| Extrinsic (time) value | Premium − intrinsic value |
| Rupee P&L | Per-share P&L × lot size × lots |
Spreads & Iron Condor
| Vertical spread max profit (debit) | Strike width − net debit |
|---|---|
| Vertical spread max loss (debit) | Net debit paid |
| Iron Condor net credit | Premiums received − premiums paid |
| Iron Condor max loss | Wider wing width − net credit |
| Iron Condor breakevens | Short put − credit · Short call + credit |
Greeks (Black-Scholes)
| Delta | Call Δ = N(d₁) · Put Δ = N(d₁) − 1 |
|---|---|
| Gamma | Γ = n(d₁) / (S · σ · √T) |
| Theta | Θ_call = −(S·n(d₁)·σ)/(2√T) − r·K·e^(−rT)·N(d₂) (per year; ÷365 per day) |
| Vega | ν = S · n(d₁) · √T (per 1.00 vol; ÷100 for per 1%) |
| Rho | ρ_call = K · T · e^(−rT) · N(d₂) · ρ_put = −K · T · e^(−rT) · N(−d₂) |
| Vanna | Vanna = ∂Δ/∂σ = ∂ν/∂S = −n(d₁) · d₂ / σ |
| Charm | Charm = ∂Δ/∂t = −n(d₁) · (2rT − d₂σ√T) / (2Tσ√T) |
| Vomma | Vomma = ν · (d₁ · d₂) / σ |
Risk & probability
| Position size (lots) | (Capital × risk %) ÷ max loss per lot |
|---|---|
| Reward-to-risk | Max profit ÷ max loss |
| Breakeven win-rate | Max loss ÷ (max profit + max loss) |
| Expected value | (Win% × max profit) − (loss% × max loss) |
S = underlying price, K = strike. See our Methodology for models and assumptions, and put these to work in the calculators.
Frequently Asked Questions
What is the breakeven formula for options?
For a long call, breakeven = strike + premium paid. For a long put, breakeven = strike − premium paid. For multi-leg strategies, breakeven is any price where the combined payoff equals zero.
How do you calculate option position size?
Position size in lots = (trading capital × risk % per trade) ÷ maximum loss per lot. This ties every position to your capital and the specific trade's risk.
What is the expected value formula for a trade?
Expected value = (win probability × maximum profit) − (loss probability × maximum loss). A positive expected value with a realistic win rate is the goal.
Educational content only — not investment advice. Figures are illustrative; confirm live specifications on the NSE.