GEVORDERD · DERIVATEN & ALGO

Options Greeks

Delta, Gamma, Theta, Vega - the sensitivities that drive options pricing.

Calls, puts, strike price en expiratie: de basis van optiehandel.

Why Greeks Matter

Options are not stocks. Their price depends on multiple factors simultaneously: the underlying price, time to expiration, implied volatility, and interest rates. The Greeks measure how sensitive an option's price is to changes in each of these factors.

Without understanding the Greeks, you're flying blind. You might buy a call expecting to profit from a price increase, only to lose money because time decay (Theta) or a volatility drop (Vega) ate your premium faster than the price moved in your favor.

Delta (Δ) - Directional Sensitivity

Delta measures how much an option's price changes for a $1 move in the underlying.

Call delta ranges from 0 to +1. A delta of 0.50 means the option gains ~$0.50 for every $1 the stock rises.
Put delta ranges from 0 to -1. A delta of -0.50 means the option gains ~$0.50 for every $1 the stock falls.
At-the-money (ATM) options have delta near ±0.50.
Deep in-the-money (ITM) options have delta near ±1.00 (they behave almost like stock).
Far out-of-the-money (OTM) options have delta near 0 (they barely move with the stock).

Delta as probability proxy: Delta roughly approximates the probability that the option expires in-the-money. A 0.30 delta call has roughly a 30% chance of expiring ITM. This is an approximation, not exact, but useful for intuition.

Gamma (Γ) - Rate of Delta Change

Gamma measures how much delta changes for a $1 move in the underlying. It's the "acceleration" of an option's price sensitivity.

Gamma is highest for ATM options near expiration.
High gamma means delta changes rapidly - the option becomes very sensitive to small price moves.
This is why short-dated ATM options are "explosive" - small moves in the stock cause large swings in the option price.

Gamma risk: Selling short-dated ATM options exposes you to extreme gamma risk. A sudden move can cause massive losses because delta shifts rapidly against you. This is one of the most dangerous positions in options trading.

Theta (Θ) - Time Decay

Theta measures how much an option's price decreases per day, all else being equal. It represents the "cost of time."

All options lose value as time passes (assuming nothing else changes). This is time decay.
Theta accelerates as expiration approaches - the last 30 days see the fastest decay.
Option buyers are "paying" theta every day. Option sellers are "collecting" theta every day.
ATM options have the highest theta. Deep ITM and far OTM options have lower theta.

Theta is the reason why buying options is a race against time. You need the underlying to move enough, fast enough, to overcome the daily theta bleed.

Vega (ν) - Volatility Sensitivity

Vega measures how much an option's price changes for a 1% change in implied volatility (IV).

When IV increases, all options become more expensive (higher vega = bigger effect).
When IV decreases, all options become cheaper.
Longer-dated options have higher vega (more time for volatility to matter).
ATM options have the highest vega.

IV Crush: After major events (earnings, Fed meetings), implied volatility often drops sharply. Even if the stock moves in your direction, the IV crush can cause your option to lose value. This is the most common way beginners lose money on earnings plays.

Greeks Interaction

The Greeks don't operate in isolation. They interact:

Scenario	Greeks at play	Net effect
Stock rises, IV drops	+Delta, -Vega	Gains from delta may be offset by vega loss
Stock flat, time passes	-Theta	Pure time decay loss for buyers
Stock moves sharply near expiry	High Gamma	Delta shifts rapidly, large P&L swings
IV spikes before event	+Vega	All options gain value regardless of direction

Practical Framework

Buying options: You are long gamma, long vega, short theta. You need a move (gamma) or a vol increase (vega) to overcome time decay (theta).
Selling options: You are short gamma, short vega, long theta. You profit from time passing and vol decreasing, but you're exposed to large moves.

Every options trade is a bet on some combination of direction, time, and volatility. The Greeks quantify each component.

Practice

Exercise 1

An ATM call has delta 0.50, theta -0.05, vega 0.10. The stock rises $2 but IV drops 3%. Estimate the option's price change: (+$1.00 from delta) + (-$0.05 from theta) + (-$0.30 from vega) = approximately +$0.65. The directional gain was partially offset by the IV drop.

Exercise 2

Explain in your own words why buying a call before earnings is risky even if you're right about the direction.

Key Takeaways

Delta = directional exposure. Gamma = how fast delta changes.
Theta = daily time decay cost. Vega = volatility sensitivity.
Buying options: need movement or vol increase to overcome theta.
Selling options: profit from time and vol decrease, risk from large moves.
IV crush after events can negate directional gains.

Wat zijn opties?

Opties zijn contracten die je het recht (maar niet de plicht) geven om een onderliggende asset te kopen of verkopen tegen een vooraf bepaalde prijs, op of voor een bepaalde datum.

Call-optie: Het recht om te kopen.
Put-optie: Het recht om te verkopen.
Strike price: De prijs waartegen je kunt kopen/verkopen.
Expiratie: De datum waarop het contract afloopt.

Belangrijkste punten

Opties geven rechten, geen verplichtingen (voor de koper).
De premie is de prijs die je betaalt voor het contract.
Opties kunnen worden gebruikt voor speculatie, hedging en inkomen.
Tijdsverval werkt tegen de koper van opties.

Les afgerond

Je hebt afgerond: Options Greeks.