Options and Greeks

Option — is a contract that gives the buyer the right (but not the obligation) to buy (call option) or sell (put option) the underlying asset at a predetermined price (strike price) before or on a specified date (expiration date). For this right, the buyer pays the seller a premium. The asymmetry of rights and obligations is the key distinction between options and futures: the option buyer has limited loss (only the premium) but unlimited potential profit.

Option styles: American — exercised on any day before expiration; European — only on the expiration date. Option statuses relative to the strike: In-the-money (ITM) — the option has intrinsic value (call: spot > strike; put: strike > spot); At-the-money (ATM) — spot is approximately equal to strike; Out-of-the-money (OTM) — no intrinsic value. Option premium = Intrinsic Value + Time Value.

The Black-Scholes model is the primary analytical model for pricing European options. Key variables: underlying asset price, strike price, time until expiration, risk-free rate, volatility. Practice shows that real markets deviate from the model's assumptions — there is a volatility smile, where implied volatility is higher for out-of-the-money options.

Greeks are indicators of option price sensitivity to changes in factors. Delta: change in option price for a 1-unit change in price of the underlying asset. Delta for calls ranges from 0 to 1; puts from -1 to 0. An ATM option has a delta around 0.5. Delta hedging: maintaining a delta-neutral position. Gamma: rate of change of delta. High gamma for ATM options near expiration indicates the risk of sharp movements. Theta: time decay — how much the option loses in one day, all else equal. Option buyers pay theta, sellers collect. Vega: sensitivity to changes in implied volatility. Long options means long vega.

Main option strategies: Covered Call — long stock plus short call (income generation); Protective Put — long stock plus long put (portfolio insurance); Straddle — long call plus long put at one strike (betting on high volatility); Collar — buy put plus sell call (free or low-cost insurance). Implied Volatility — volatility embedded in the market price of the option; VIX — the "fear index," calculated as the implied volatility of the S&P 500 index.