Sonith ManakkatAfter the basics of options, people meet a row of Greek letters. They sound frightening but each answers a simple question: if one thing changes, roughly how much does the option price react? This part uses a car dashboard as the picture, then an Expert view gives the standard definitions. All numbers are illustrative.
The dashboard idea
- 0.50delta
- 0.04gamma
- -0.05theta per day
- 0.12vega per 1 point of volatility
The next sections read each dial in turn.
- 1One input changesThe underlying price, the time left or the uncertainty
- 2Read the matching dialDelta for price, theta for time, vega for uncertainty
- 3Dial times the changeA small change times the dial gives a rough price change
- 4Others held stillThe reading assumes nothing else moves
- 5Real moves mixInputs move together, so the effects combine
Takeaway. A Greek is a rate: a change in one input times its dial gives a rough change in the price.
Delta: how much the price tends to move
- DeltaChange in the option price for a 1 unit move in the underlying
For example, with a share priced at 100 and a call delta of 0.50 (illustrative), a move to 101 would lift the option price by roughly 0.50. A call far out of the money has a delta near 0; one deep in the money has a delta near 1.
Some people read delta as a rough chance that the option finishes in the money. Treat that with caution: it is a loose reading of the number, not a probability forecast.
Expert viewDelta, precisely
Delta is the first partial derivative of the option price with respect to the underlying price. It is also used to size the quantity of the underlying that offsets an option's price sensitivity, a practice called delta hedging, which needs frequent adjustment because delta moves. Delta is a local measure: it describes tiny moves around the current price, and for larger moves it becomes less accurate.
Gamma: how fast delta changes
Delta
- The speed: how much the price reacts now
- First-order sensitivity
Gamma
- The acceleration: how quickly delta itself changes
- Biggest near the strike and near expiry
Expert viewGamma, precisely
Gamma is the second partial derivative of the option price with respect to the underlying price, or the rate of change of delta. It is usually highest for options near the strike with little time left. A buyer of an option has positive gamma; a seller has negative gamma, which means the seller's exposure can change unfavourably when the underlying moves sharply.
Theta: the clock
- ThetaChange in the option price as one day passes
Expert viewTheta, precisely
Theta is the partial derivative of the option price with respect to time. Quoted per day or per year depending on the platform, so check the unit. It is not constant: for options near the strike it tends to grow in size close to expiry. For a long option it is usually negative, because time value fades.
Vega and implied volatility
- VegaChange in the option price for a 1 point change in implied volatility
First, volatility. It is a number describing how widely a price swings. Historical volatility looks backward: how much did the price actually move over a past window? Implied volatility looks at today's option price and asks: what level of volatility would the pricing model need to produce this price? It is backed out of the price, the way you can work out the interest rate from a loan repayment.
Historical
- Measured from past price moves
- A fact about the past
Implied
- Backed out of today's option price
- The market's nervousness as a number
- News raises uncertaintyWider outcomes now look possible
- Implied volatility risesOption prices are pushed up
- Premium growsWhile the underlying stays where it was
- Vega measures itPrice change per 1 point of implied volatility
Implied volatility is not a forecast and not a promise. It reflects what the market is willing to pay for protection or exposure today, and it can differ across strikes and expiry dates.
Expert viewVega, rho and the model behind them
Vega is the partial derivative of the option price with respect to volatility (strictly not a Greek letter, but conventionally grouped with them). It is generally larger for options with more time left. Rho is the partial derivative with respect to the interest rate; it is usually the smallest effect for short-dated options and is mentioned for completeness.
These definitions come from the classic family of option pricing models. Such a model takes inputs (underlying price, strike, time, rate, volatility) and outputs a price, resting on assumptions: smooth price paths, constant volatility, no costs, no jumps. Real markets break these assumptions, so implied volatility is best read as a quoting convention that converts a price into a comparable number, not as a measurement of truth.
Takeaway. Implied volatility is worked backwards from the price, like finding a rate from a repayment.
Reading the dials together
- Price rises 1 unitDelta adds about 0.50, gamma nudges delta up
- One day passesTheta takes away about 0.05
- Uncertainty rises 1 pointVega adds about 0.12
- Net effectThe three combine, and may partly cancel out
- 1How does the price react to a 1 unit move in the underlying?Yes Delta.No keep going
- 2How fast does delta itself change?Yes Gamma.No keep going
- 3What does one passing day do to the price?Yes Theta.No keep going
- 4What if implied volatility rises by 1 point?Yes Vega.No keep going
- 5What if the interest rate changes?Yes Rho, usually the smallest effect for short-dated options.No keep going
- 6OtherwiseNone of them covers a big move or several changes at once, because each is local.
Takeaway. Each Greek answers one narrow question, so none is a forecast.
The limits of the dials
- They are localValid for small changes around today's levels
- They changeDelta, gamma and others move as price and time move
- Inputs interactPrice, time and volatility move together, not one at a time
- Models simplifyThey rest on assumptions real markets break
Delta is the exact chance of a gain
It is a sensitivity that is sometimes read as a rough probability, with caution
High implied volatility means the price will move a lot
It reflects what the market is pricing in today, not a certain outcome
The Greeks are dials, not forecasts: each one shows a sensitivity at this moment.
Frequently asked questions
Why does an option get dearer when the price has not moved?
Because implied volatility can rise, which lifts time value. Vega measures this.
Is implied volatility a prediction?
No. It is what the market's pricing implies today, and it may turn out different from what actually happens.
Do I need to know all the Greeks?
This article is education only. It explains what the dials mean, nothing more.
Are the numbers real?
No. All values are illustrative.