Options
An option grants the right (not the obligation) to buy (call) or sell (put) an underlying at a strike price before or at expiry. You pay or collect premium; P&L depends on the underlying, time, and implied volatility — see Contract types for context, then Black-Scholes and Volatility for valuation.
Vanilla calls and puts
| Type | Position | View | Payoff (at expiry) | Notes |
|---|---|---|---|---|
| Call | Long (buyer) | Bullish | Profit if S > K; loss capped at premium if S ≤ K | Directional leverage; negative theta for buyer |
| Call | Short (seller) | Neutral / mildly bearish | Premium received; unlimited downside if S rallies hard | Often covered with long underlying (covered call) |
| Put | Long (buyer) | Bearish / hedge | Profit if S < K; loss capped at premium if S ≥ K | Portfolio insurance (protective put) |
| Put | Short (seller) | Neutral / mildly bullish | Premium received; large loss if S drops sharply | Tail risk; often tied to cash-secured or covered structures |
Call / put visualization
100.00
100.00
0.25 yr
5.0 %
20 %
Greeks (position)
0.5695
0.0393
-0.0287
0.1964
Premium at entry (S = current spot): 4.6150
Sensitivities (Greeks)
| Greek | Variable | Effect (intuition) | Notes |
|---|---|---|---|
| Delta (Δ) | Underlying price | Instantaneous directional exposure (~ ITM probability in rough terms) | 0 to 1 for long call; long put: negative delta |
| Gamma (Γ) | Delta | Rate of change of delta | Often peaks near strike as expiry approaches |
| Theta (Θ) | Time | Time decay of option value | Negative for long options; positive for short options |
| Vega (ν) | Implied vol | Sensitivity to a vol shock | Long vol = long vega; relevant for straddle/strangle |
Common strategies
| Strategy | Legs | Exposure (Greeks) | P&L profile (sketch) | Notes |
|---|---|---|---|---|
| Covered call | Long underlying + short call | Δ+, Γ−, Θ+, ν− | Premium income; upside capped above strike | Income in sideways markets; give up extreme upside |
| Protective put | Long underlying + long put | Δ+, Γ+, Θ−, ν+ | Loss floored below strike (minus premium); upside retained | Ongoing insurance cost if rolled |
| Bull call spread | Long lower-strike call + short higher-strike call | Δ+, Γ≈0, Θ−, ν+ (low) | Capped gain; loss limited to net debit | Cheaper than naked call |
| Bear put spread | Long higher-strike put + short lower-strike put | Δ−, Γ≈0, Θ−, ν+ (low) | Capped gain; limited loss | Logical mirror of bull call spread |
| Long straddle | Long call + long put (same strike, same expiry) | Δ≈0, Γ+, Θ−, ν+ | Loss if S near strike; profit if move is large enough | Long volatility; time decay headwind |
| Long strangle | Long OTM call + long OTM put | Δ≈0, Γ+, Θ−, ν+ | Wider loss zone; needs a bigger move | Often before earnings / binary events |
| Short straddle | Short call + short put (same strike) | Δ≈0, Γ−, Θ+, ν− | Max profit if S = strike; unlimited risk on large moves | Experienced traders only; high margin |
| Iron condor | Put spread + call spread (OTM strikes) | Δ≈0, Γ−, Θ+, ν− | Net credit if S between wings; loss capped | Popular short-vol structure; watch tails |
| Iron butterfly | Short straddle + OTM wings | Δ≈0, Γ−, Θ+, ν− | Max profit if S = center strike; wings cap risk | Condor « pinched » around ATM strike |
| Calendar spread | Long far expiry + short near expiry (same strike) | Δ≈0, Γ±, Θ±, ν+ | Sensitive to vol term structure | Exposure highly maturity-dependent; validate signs per trade |
Practical reminders
ITM / ATM / OTM: in-the-money, at-the-money, out-of-the-money vs spot and strike.
American vs European style (option contract terms, not geography): American = exercise allowed before expiry; European = exercise only at expiry. E.g. many US single-stock options are American-style; many index options (SPX, Euro Stoxx…) are European-style — including on US underlyings.
Contract multiplier: US equity options often × 100; check specs per market.
To add: payoff diagrams, numeric straddle example, option chain / skew notes.