← All lessons Track 02 · Derivatives · Lesson 2.2

What are options? The Greeks and IV

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An option is a contract that gives you the right, but not the obligation, to buy or sell something at a set price before a set date. You pay a premium for that right.

Calls and puts

  • A call is the right to buy at the strike price. It gains value when the share rises.
  • A put is the right to sell at the strike price. It gains value when the share falls.

One US equity option usually covers 100 shares. When you buy an option, the most you can lose is the premium. That's the appeal: defined risk with leverage.

Long callLong put StrikeShare price at expiry → ProfitLoss Max loss = premium paid
Payoff at expiry for one call and one put at the same strike, after the premium.

What sets the price

An option's premium is made of two parts. Intrinsic value is what it would be worth if exercised now. Extrinsic value is everything else: the value of time and of uncertainty. The Greeks describe how that premium reacts when things change.

Price, time and value together

70100 (strike)1301y6mExpiryShare priceTime to expiryCall value
A call’s value across share price and time. Far from expiry the curve is smooth; at expiry it collapses into the hockey stick. The gap between them is time value, and it is what theta erodes.

The Greeks

GreekMeasuresRule of thumb
Delta (Δ)Change in option price for a $1 move in the shareCalls 0 to 1, puts −1 to 0. Roughly the odds of finishing in the money.
Gamma (Γ)Change in delta for a $1 moveHighest at the money and near expiry.
Theta (Θ)Value lost per day from time passingNegative for buyers, positive for sellers. Speeds up near expiry.
Vega (ν)Change in price for a 1 point move in IVBiggest for long-dated, at-the-money options.
Rho (ρ)Change in price for a 1% move in ratesUsually small, matters more for long-dated options.

The useful way to think about them: delta is your directional exposure, gamma is how fast that exposure changes, theta is the rent you pay (or collect) each day, and vega is your bet on volatility itself.

Last 30 days Time value90 days to expiryExpiry
Theta in practice: an at-the-money option loses time value slowly at first, then quickly into expiry.

Implied volatility (IV)

IV is the volatility the market is pricing in. It's backed out of the option price, not measured from history. High IV means expensive options, because the market expects big moves. Low IV means cheap options.

2 weeks out1 week out Day beforeDay after IV peaksCrush
Illustrative implied volatility around an earnings release.

IV typically rises before known events like earnings and collapses straight after, which is called IV crush. That's why you can be right on direction and still lose money buying options: the drop in IV can outweigh the move.

Putting it together

Before buying any option, ask three things. Do I expect a move bigger than the premium implies? Will it happen before theta eats the position? And is IV already pricing it in? If the answer to any is no, the trade probably isn't worth it.

Educational content only, not financial advice. Options involve significant risk and are not suitable for everyone.

Sources (2)
  1. Nobel Prize: Economic Sciences 1997 (Merton and Scholes)
  2. Cboe: VIX methodology
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