Options and derivatives

An option is a contract about the future price of something else, which makes it the one instrument where you can be precise about WHICH part of a view you hold: direction, timing, magnitude, or volatility itself. Professionals use that precision to shape risk. Amateurs use the leverage to rent lottery tickets. Same instrument, opposite trades.

The contracts

The two primitives

CALL: the right (not obligation) to BUY at the strike price by expiry
PUT:  the right (not obligation) to SELL at the strike price by expiry

buyer pays a premium, risks only the premium, and has the choice;
seller collects the premium, and has the obligation if exercised

payoff at expiry:
  long call = max(0, price - strike) - premium
  long put  = max(0, strike - price) - premium

Everything else in the listed-options world (spreads, collars, straddles) is these two primitives combined. A futures contract, by contrast, is an obligation on both sides: no premium, no choice, linear payoff, and the standard instrument for rates, commodities and index exposure.

What an option costs, and why: volatility

An option's value has two parts: intrinsic value (what exercising now would be worth) and time value (the value of the remaining possibility). Time value is where the interesting economics live, and its main driver is expected movement: the more the underlying might travel before expiry, the more the right to choose is worth. Run the logic backwards and every option price contains a forecast: the implied volatility the market is charging. Comparing implied volatility to what the asset actually realizes is the entire volatility-trading industry in one sentence, and its long-run finding, that implied usually runs a little above realized, is the volatility risk premium: options, like insurance, cost slightly more than they pay out on average, because sellers bear the tail.

The Greeks: the risk dials

Greek	Measures sensitivity to	In practice
Delta	The underlying's price	Share-equivalent exposure; a 0.30-delta call behaves like 30 shares per contract
Gamma	Delta itself changing	How fast exposure snowballs as the move happens; highest near the strike, near expiry
Theta	Time passing	The daily rent a buyer pays and a seller collects
Vega	Implied volatility	P&L from the fear gauge moving, price unchanged
Rho	Interest rates	Minor for short-dated; real for LEAPS

A position's Greeks say exactly what you are long and short of: a bought call is long direction (delta), long the move accelerating (gamma), short time (theta), long fear (vega). Professionals choose structures BY the Greeks: the question is never "calls or puts?" but "which risks do I want to own and which am I willing to sell?"

The honest uses

Hedging. A put under a concentrated position is insurance with a known premium and a chosen deductible (the strike). A collar (buy the put, fund it by selling a call) trades away upside for cheap downside protection: the standard structure for a founder's stock or an outsized winner.
Defined-risk expression. A call spread (buy one strike, sell a higher) caps both cost and payoff: the instrument for "I think it rises to ABOUT 120 by March", priced at a fraction of the shares.
Income with obligations attached. Covered calls and cash-secured puts sell time value against positions you hold or want. The premium is real; so is the obligation. Selling a put IS agreeing to buy the stock lower, and the premium is fair pay only if you wanted to.
Event positioning. Straddles and strangles buy movement without direction, for when the thesis is "this earnings print resolves something big" rather than which way.

The amateur pattern, named

Short-dated out-of-the-money calls are the most bought and worst performing retail instrument: maximal theta bleed, minimal probability, and implied volatility typically most expensive exactly when the story is most exciting. The structural edge in listed options has historically sat with disciplined SELLERS of richly priced insurance, not buyers of cheap-looking lottery tickets. When you buy an option, you are paying the volatility risk premium; the thesis must clear that bar too.

Mechanics that bite

Liquidity lives at round strikes and near months. Wide bid-ask spreads on far strikes quietly cost more than theta.
Assignment is real. Short in-the-money options can be exercised against you, especially around dividends.
IV crush. Implied volatility collapses after the event it was pricing; a correct directional call on earnings can still lose if the move was smaller than the implied straddle. The pre-event question is always: what move is ALREADY priced?
Leverage discipline. Notional exposure, not premium paid, is the size of the position. Professionals size by delta-adjusted notional and worst-case loss, never by "it is only the premium".

Glossary for this guide

Call option: The right, without obligation, to buy at the strike price by expiry. Upside exposure for a known premium; the seller takes the obligation side.
Put option: The right, without obligation, to sell at the strike by expiry: insurance on a price. Under a concentrated position it sets a floor for a known premium.
Strike price: The contracted transaction price of an option: the deductible on the insurance. Choosing it is choosing how much pain you self-insure before protection starts.
Premium: What the option buyer pays and the seller keeps regardless of outcome. The buyer's maximum loss and the seller's maximum gain.
Intrinsic vs time value: Intrinsic value is what exercising now would be worth; time value is the price of the remaining possibility. Time value bleeds to zero at expiry, which is theta made visible.
Implied volatility: The movement forecast embedded in an option's price: run the pricing model backwards and out it comes. Comparing it to what the asset then actually does is the entire volatility trade.
Volatility risk premium: The long-run finding that implied volatility usually exceeds realized: options, like insurance, cost a bit more than they pay out on average, because sellers bear the tail. Buyers' theses must clear this bar.
Delta: An option's share-equivalent exposure: a 0.30-delta call behaves like 30 shares per contract. Professionals size option positions by delta-adjusted notional, never by premium paid.
Gamma: How fast delta itself changes as the underlying moves: the snowball rate of exposure. Highest near the strike close to expiry, where hedging it forces dealers to chase the market.
Theta: The daily cost of time passing: what option buyers pay in rent and sellers collect. Short-dated out-of-the-money options are almost all theta.
Vega: Sensitivity to implied volatility: profit and loss from the fear gauge moving with price unchanged. Long options are long fear; short options are short it.
Collar: Buy a protective put, fund it by selling a call above: downside floor purchased with surrendered upside. The standard dressing for a concentrated winner.
Covered call: Selling a call against shares you own: income now in exchange for capping the upside. Fair pay only when you would have been content to sell at the strike anyway.
Straddle: Buying the call and the put at the same strike: a bet on movement without direction. Its price before an event states, in dollars, the move the market already expects.
IV crush: The collapse of implied volatility once the awaited event passes. A correct directional call on earnings can still lose money if the move was smaller than what the straddle had priced.
Assignment: Being exercised against on a short option: the obligation arriving. In-the-money shorts get assigned, especially around dividends, and the shares change hands whether convenient or not.

Options and derivatives

The contracts

The two primitives

CALL: the right (not obligation) to BUY at the strike price by expiry
PUT:  the right (not obligation) to SELL at the strike price by expiry

buyer pays a premium, risks only the premium, and has the choice;
seller collects the premium, and has the obligation if exercised

payoff at expiry:
  long call = max(0, price - strike) - premium
  long put  = max(0, strike - price) - premium

What an option costs, and why: volatility

The Greeks: the risk dials

Greek	Measures sensitivity to	In practice
Delta	The underlying's price	Share-equivalent exposure; a 0.30-delta call behaves like 30 shares per contract
Gamma	Delta itself changing	How fast exposure snowballs as the move happens; highest near the strike, near expiry
Theta	Time passing	The daily rent a buyer pays and a seller collects
Vega	Implied volatility	P&L from the fear gauge moving, price unchanged
Rho	Interest rates	Minor for short-dated; real for LEAPS

The honest uses

Hedging. A put under a concentrated position is insurance with a known premium and a chosen deductible (the strike). A collar (buy the put, fund it by selling a call) trades away upside for cheap downside protection: the standard structure for a founder's stock or an outsized winner.

Defined-risk expression. A call spread (buy one strike, sell a higher) caps both cost and payoff: the instrument for "I think it rises to ABOUT 120 by March", priced at a fraction of the shares.

Income with obligations attached. Covered calls and cash-secured puts sell time value against positions you hold or want. The premium is real; so is the obligation. Selling a put IS agreeing to buy the stock lower, and the premium is fair pay only if you wanted to.

Event positioning. Straddles and strangles buy movement without direction, for when the thesis is "this earnings print resolves something big" rather than which way.

The amateur pattern, named

Mechanics that bite

Liquidity lives at round strikes and near months. Wide bid-ask spreads on far strikes quietly cost more than theta.

Assignment is real. Short in-the-money options can be exercised against you, especially around dividends.

IV crush. Implied volatility collapses after the event it was pricing; a correct directional call on earnings can still lose if the move was smaller than the implied straddle. The pre-event question is always: what move is ALREADY priced?

Leverage discipline. Notional exposure, not premium paid, is the size of the position. Professionals size by delta-adjusted notional and worst-case loss, never by "it is only the premium".

Glossary for this guide

Call option: The right, without obligation, to buy at the strike price by expiry. Upside exposure for a known premium; the seller takes the obligation side.
Put option: The right, without obligation, to sell at the strike by expiry: insurance on a price. Under a concentrated position it sets a floor for a known premium.
Strike price: The contracted transaction price of an option: the deductible on the insurance. Choosing it is choosing how much pain you self-insure before protection starts.
Premium: What the option buyer pays and the seller keeps regardless of outcome. The buyer's maximum loss and the seller's maximum gain.
Intrinsic vs time value: Intrinsic value is what exercising now would be worth; time value is the price of the remaining possibility. Time value bleeds to zero at expiry, which is theta made visible.
Implied volatility: The movement forecast embedded in an option's price: run the pricing model backwards and out it comes. Comparing it to what the asset then actually does is the entire volatility trade.
Volatility risk premium: The long-run finding that implied volatility usually exceeds realized: options, like insurance, cost a bit more than they pay out on average, because sellers bear the tail. Buyers' theses must clear this bar.
Delta: An option's share-equivalent exposure: a 0.30-delta call behaves like 30 shares per contract. Professionals size option positions by delta-adjusted notional, never by premium paid.
Gamma: How fast delta itself changes as the underlying moves: the snowball rate of exposure. Highest near the strike close to expiry, where hedging it forces dealers to chase the market.
Theta: The daily cost of time passing: what option buyers pay in rent and sellers collect. Short-dated out-of-the-money options are almost all theta.
Vega: Sensitivity to implied volatility: profit and loss from the fear gauge moving with price unchanged. Long options are long fear; short options are short it.
Collar: Buy a protective put, fund it by selling a call above: downside floor purchased with surrendered upside. The standard dressing for a concentrated winner.
Covered call: Selling a call against shares you own: income now in exchange for capping the upside. Fair pay only when you would have been content to sell at the strike anyway.
Straddle: Buying the call and the put at the same strike: a bet on movement without direction. Its price before an event states, in dollars, the move the market already expects.
IV crush: The collapse of implied volatility once the awaited event passes. A correct directional call on earnings can still lose money if the move was smaller than what the straddle had priced.
Assignment: Being exercised against on a short option: the obligation arriving. In-the-money shorts get assigned, especially around dividends, and the shares change hands whether convenient or not.