Greeks in practice - delta hedging

Options are not direction. Options are exposure to time, volatility and movement. The Greeks are the language you use to describe that exposure. Without the Greeks you trade intuition. With the Greeks you trade a portfolio of exposures that you can measure and hedge. Delta hedging is the basic technique for controlling the first of those exposures — direction.

The goal of this lesson is not an academic definition of the Greeks. The goal is to show you how to read them in a platform, how to calculate the real risk and how to build a delta-neutral position.

What the Greeks really measure

Every Greek is a derivative. It measures how much the option price changes when one market parameter changes, assuming everything else stays put.

Reading example: a Call option with 100 days to expiry, Delta 0.35, Gamma 0.02, Theta -0.08, Vega 0.22. That means: it behaves like 35 shares per 100 contracts, for every 1 USD of upside Delta grows to 0.37, every day you lose 0.08 USD to time, and a 1% rise in IV lifts the option by 0.22 USD.

Portfolio delta and the stock equivalent

This is the key formula for managing a position.

Position Delta = Option Delta * Number of Contracts * Multiplier (usually 100) * Direction (+1 long, -1 short)

Example:
Long 2x Call Delta 0.60 = 0.60 * 2 * 100 = +120 delta = equivalent to long 120 shares
Short 1x Call Delta 0.30 = -0.30 * 1 * 100 = -30 delta = equivalent to short 30 shares

Portfolio Delta = Sum of all deltas
Stock equivalent = Portfolio Delta

Option price ≈ Delta * Move in the underlying (+ 0.5 * Gamma * Move^2) // approximation

If your Portfolio Delta is +150 on SPY, then when SPY rises by 1 USD your portfolio gains about 150 USD, no matter how many options you have open.

Gamma: why delta is not constant

A beginner thinks a Delta of 0.50 is forever. Gamma shows that this is a lie.

New Delta ≈ Old Delta + Gamma * Move in the underlying

Example:
Delta = 0.50, Gamma = 0.05, Move = +3 USD
New Delta = 0.50 + 0.05 * 3 = 0.65

Your exposure grew by 30% without any decision from you.

High Gamma shows up in ATM options close to expiry. That is where delta hedging becomes expensive and necessary. Low Gamma (far OTM or long DTE) = stable Delta, easier to hold.

Delta hedging in practice - step by step

Delta hedging means bringing the Portfolio Delta to zero (or to a defined target) through a transaction in the underlying or in another option.

Assume this: you sold 10x Iron Condor on SPX, your Portfolio Delta is +25. The market is rising and you do not want a directional bet.

Step 1: Calculate the delta
Portfolio Delta = +25

Step 2: Calculate the hedge
You need -25 delta.
If you hedge with stock / ETF: Sell 25 SPY shares (or futures: -25 / futures delta)

Step 3: Hedge and measure the cost
Hedge cost = commission + slippage
New Delta = +25 + (-25) = 0

Step 4: Re-hedge at a threshold
Set a threshold: "I re-hedge when |Portfolio Delta| > 30"
Do not hedge every tick. That will kill you with commissions. Measure.

A professional market maker does this automatically. A retail trader does it once or twice a day, or when a threshold is breached.

Two styles:

• Hedging with stock: Simple, precise, but it requires capital and generates commissions.
• Hedging with an option: For example buying a cheap long call to offset negative delta. It also changes Gamma/Vega, so it is harder.

Theta and Vega as payment for risk

When you are delta-neutral, your P&L is governed by Theta and Vega, and by Gamma.

Approximate daily P&L for a delta-neutral portfolio:
P&L ≈ Theta + 0.5 * Gamma * (Move)^2 + Vega * Change in IV

If you have +Gamma (long options), you earn on large moves.
If you have -Gamma (short options), you lose on large moves and you earn on Theta.

This is the fundamental trade-off of income strategies: you sell options (negative Gamma, positive Theta) and you have to decide whether the Gamma risk is worth the Theta income.

Measure the ratio:

Theta/Gamma ratio = daily Theta / (0.5 * Gamma * (1% move)^2)

If you earn 20 USD a day on Theta but a 1% move costs you 50 USD through Gamma, you have an unfavourable profile in a volatile market.

When the plan says do not trade

1. When you do not understand your Portfolio Delta before opening. If the platform shows you a delta and you do not know what +80 delta means on a 5k USD account, do not open. It is like driving without a speedometer.
2. When your position Gamma > 2x Theta per 1% move. You are in a gamma trap. A small move wipes out a week of Theta in minutes. Especially 0-3 DTE ATM.
3. When you are delta-neutral but Vega = 60% of your account value for a 5% change in IV. Around earnings IV drops by 20-40%. You will go broke on Vega even though Delta was zero.
4. When the bid/ask spread on the hedge > 30% of your daily Theta. You are trying to save 10 USD on Delta and losing 25 USD on slippage. A bad market for hedging (night, low volume on the WIG20).
5. When you have no defined re-hedge threshold. Hedging “by eye” is a guarantee of overtrading. Without a threshold (for example |Delta| > 30 or > 5% of capital) do not hedge.

Mistakes that cost the most

Measurable exercise

Title: 14-day Greeks journal

1. Choose 1 liquid ticker (for example SPY, QQQ, WIG20 ETF). On a demo platform open 1 spread: Bull Put Spread 30 DTE, 0.15-0.20 Delta short leg.
2. Every day at 16:00 (after the close of the Warsaw Stock Exchange, GPW) or 22:00 (USA) record in a table: Date | Underlying price | Portfolio Delta | Gamma | Daily Theta | Vega | P&L of the day | Hedge action (YES/NO).
3. Set the rules up front: hedge to 0 when |Delta| > 25. Hedge with stock/ETF. Record the commission cost of the hedge.
4. After 14 days calculate: Total Theta / Total hedge costs + slippage / Max Delta / Max daily loss from Gamma. Answer: did Theta cover 2x the hedge costs?

Pass criterion: 14 entries + a calculated Theta efficiency ratio. Without that you do not know whether an income strategy is actually profitable.

Check yourself

1. You are Long 3x Call Delta 0.70 and Short 2x Call Delta 0.40 on the same underlying, multiplier 100. What is the Portfolio Delta and what does it mean?
2. Your position Gamma is -0.08, Delta is 0. You get a 5 USD drop on SPY. How much does Delta change and what does that mean for hedging?
3. Why does a short premium position have positive Theta but negative Gamma? Explain the trade-off.
4. Your Delta is +40 and you want to get to 0 by hedging with stock. What do you do?
5. What is a re-hedge threshold and why is continuous hedging unprofitable for a retail trader?

Frequently asked questions

Do I have to be delta-neutral all the time? No. Delta-neutral is a tool, not a goal. You can deliberately run positive delta (slightly bullish) if that is your thesis. What matters is that Delta is a choice, not an accident.

Which Greek matters most for a beginner in income strategies? Delta and Theta. Delta tells you whether you have direction. Theta tells you whether you earn from time. Vega is next in line — it kills the unprepared during an IV crush. Watch Gamma when you are <7 DTE.

Can Gamma be hedged? Yes, but only with an option, not with stock. Hedging gamma requires buying/selling options with a similar Gamma. That is complex and expensive. For a retail trader it is simpler to reduce position size when Gamma is high than to hedge it.

Why does my Delta jump around in the platform? Because of Gamma and IV. On a high-volatility day Gamma rises, and Vega changes option prices, which indirectly changes delta. Measure Delta at a fixed hour and record the context (VIX / volatility).

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Educational material. This is not investment advice or a recommendation. Every trading decision is your risk. Measure exposure in dollars, not in contracts.

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