What you will learn
- Interpret a Greek using its stated units.
- Avoid treating local sensitivities as a fixed prediction.
Delta
Delta is a per-unit estimate: a call with delta 0.40 gains about HK$0.40 if the underlying rises HK$1, while a put with delta −0.40 loses about HK$0.40. Delta approaches ±1 as an option goes deeper in the money and approaches 0 when far out of the money; at the money it is roughly ±0.5.
Multiplying delta by the contract multiplier and number of contracts gives position delta, the equivalent share exposure. Delta itself changes as price, time and volatility change. Traders sometimes read it as a rough chance of finishing in the money, but that is only a heuristic.
Theta
An option's premium is intrinsic value plus time value, and theta describes how fast time value erodes. Long options usually have negative theta, which is a daily cost to the holder, while sold options have positive theta, which works in the seller's favor but comes with risk.
Decay is not linear: at-the-money options lose time value fastest in the final weeks before expiry. Textbook theta is expressed per year, so platforms divide it by 365 or 252 to quote it per day; check which. Positive-gamma positions typically carry negative theta, because convexity has a time cost.
Vega
Options bought have positive vega and gain when implied volatility rises; options sold have negative vega. Vega is largest for at-the-money options with a longer time to expiry and shrinks as expiry nears.
Units matter. Textbook vega is the price change for a 1.00 change in volatility, a move of 100 percentage points, so most platforms divide it by 100 and quote it per volatility point, for example from 25% to 26%. After an event such as earnings, implied volatility often falls sharply, which can hurt long options even when the underlying moves as hoped.
Worked example: Vega per volatility point
Illustrative: an option has vega HK$0.12 per unit per one volatility percentage point. A rise in implied volatility from 20% to 22% is two points, implying approximately HK$0.24 per unit, or HK$24 for a 100-unit contract, if other inputs are unchanged. Greeks change with price and time, and real market moves may change several inputs together.
Check your understanding
An option has delta 0.4 and the underlying rises HK$0.50. What is the first-order per-unit estimate, ignoring all other changes?
Show answer and explanation
0.4 × 0.50 = HK$0.20. This is not an exact revaluation: delta itself can change, and volatility, time and other inputs may also move.