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Summary

Theta is the daily erosion of time value — the cost of long gamma and the income of short gamma. Vega converts implied-volatility views into P&L and is the center of all volatility trading. Rho, the interest-rate greek, is negligible for short-dated options but a real planning input for LEAPS123.

Theta: Decay Curves

Position Theta Why
Long ATM option Strongly negative Maximum time value decaying, accelerating
Short ATM option Strongly positive Same decay, collected
Calendar (long back / short front) Positive Short leg decays faster
Vertical spread Small ± Legs partially offset
Iron condor / short strangle Positive Sold wings decay toward zero

Key behaviors1:

  • ATM decay is nonlinear and accelerates near expiration — a 10-day ATM call's daily decay roughly doubles in the final week; the last day erodes nearly all remaining time premium. ITM/OTM time value decays more steadily.
  • Higher IV ⇒ more premium to erode ⇒ higher theta; higher-priced stocks carry higher absolute thetas.
  • Practical conventions: "take the weekend out" on Thursday/Friday; track average daily theta = (entry premium − projected exit value) ÷ days, the holding-plan metric for long-option buyers.

Vega: Implied-Volatility Sensitivity

Vega is the value change per 1-point move in IV. A call worth 1.82 with 0.06 vega moves to ~1.88 when IV goes 17% → 18%2. Calls and puts of the same strike/month have essentially equal vegas.

  • Moneyness/time: vega tracks time value — highest ATM, shrinking as expiration approaches.
  • Long vega positions (straddles, calendars, backspreads) profit from "the rush" — IV building into events; short vega (condors, credit spreads) profits from "the crush" when events land2.
  • The double whammy: stocks fall → IV rises → a short put loses on delta and vega simultaneously; directional sellers must budget for it2.
  • IV hygiene: if a model's theoretical values sit outside the bid–ask chain-wide, the IV input is wrong — trust only IV derived from known inputs2.

Rho: When Interest Rates Matter

Rho is the value change per 1-point move in rates: calls positive, puts negative, transmitted through put–call parity. Its magnitude ≈ Strike × Rate × (Days/365), so time to expiration is the dominant driver3:

Option (ATM, ~$120 stock, 5.5% rates) Rho 25bp move ≈
38-day call +0.068 +$0.017
130-day call +0.226 +$0.057
221-day call +0.385 +$0.096
639-day LEAPS +0.638 ~16× the 38-day impact

Practical rules: ignore rho for short-dated trades; for LEAPS a 1-point rate move can be 5–8% of option value, and rate expectations are already embedded in long-dated chains. Conversions, reversals, and jelly rolls are the only pure rho vehicles — mostly professional turf3.

Links

Footnotes

  1. Passarelli, Trading Option Greeks — theta topic: decay curves, moneyness/time/IV behavior, strategy theta profiles. ↩↩

  2. Passarelli, Trading Option Greeks — vega topic: definition, behavior, rush/crush, IV-input hygiene. ↩↩↩↩↩

  3. Passarelli, Trading Option Greeks — rho topic: magnitude drivers, LEAPS, parity mechanism. ↩↩↩