Options 101

Options fundamentals

An option is an asymmetric rights contract. You are buying a “right,” not an “obligation.”

• Call: the right to buy an asset later at a fixed price
• Put: the right to sell an asset later at a fixed price

Key terms:

• Underlying: the stock/ETF (e.g. VOO, QQQ)
• Strike: the agreed buy/sell price
• Expiration
• Premium: the option’s price (what you pay or receive)
• Contract size: usually 1 contract = 100 shares

Four basic trades

This is the most important part. It is really buyer vs seller + bullish vs bearish.

Buy Call

Bet on a rally with a small amount of capital

• You think: price will go up
• Cost: pay premium
• Upside: theoretically unlimited
• Max loss: premium

Sell Call

Collect rent, but you can get squeezed

• You think: price will not rally hard

• Reward: collect premium

• Risk:

  • Naked: unlimited risk
  • Covered call: limited risk

Buy Put

The insured version of going short (defined risk)

• You think: price will go down
• Cost: premium
• Reward: the more it falls, the more you make
• Max loss: premium

Sell Put

A bit like “a limit bid to buy + collecting interest.” One of the most common strategies for long-term investors

• You think: price will not crash / you are willing to buy lower
• Reward: collect premium
• Risk: the underlying dumps (you have to take the shares)

Payoff structure

Greeks: the core of option pricing

Greeks describe how sensitive the option price is to different factors.

Delta $\Delta$ — directional sensitivity

• Meaning: if the underlying rises $1, how much the option rises

• Range:

  • Call: 0 ~ 1
  • Put: 0 ~ -1

Example:

• $\Delta$ = 0.6 → stock up $1, option up$0.6

In essence: a stand-in for position leverage

Gamma $\Gamma$ — how fast Delta changes

• Meaning: how sensitive Delta is to price changes

In essence: closer to expiration + ATM, $\Gamma$ is larger → moves get more violent

Theta $\Theta$ — time decay

• Meaning: how much value is lost each day
• The buyer’s enemy, the seller’s friend

In essence: time = how the seller gets paid

Vega $v$ — volatility sensitivity

• Meaning: how implied volatility (IV) changes affect price

In essence: IV up → options get more expensive

Rho $\rho$ — rates (secondary)

• How rate changes affect the option
• Almost irrelevant in practice

How the market prices it

Option price = intrinsic value + time value

Intrinsic value

• Call: max(0, spot − strike)
• Put: max(0, strike − spot)

Time value

Driven by three things:

• Time (longer is more expensive)
• Volatility (higher is more expensive)
• Uncertainty

The key ideas

Options are a probability game

• Sellers have a high win rate (they collect theta)
• Buyers have high payoff (they bet on a burst)

IV is the core variable

• High IV → better to sell
• Low IV → better to buy

Most options go to zero

• Theta decay is a structural edge

Sell Put ≈ buying stock on a limit

• Plus you collect a premium on top