Option
An option is a financial derivative contract that grants the buyer the right — but not the obligation — to buy (call option) or sell (put option) a specified underlying asset at a predetermined price (strike price) on or before a specified expiration date, in exchange for a premium paid to the seller at inception.
Key takeaways
- Call options profit when the underlying asset price rises above the strike; put options profit when it falls below the strike.
- The buyer pays a premium upfront; their maximum loss is limited to the premium paid.
- The seller (writer) receives the premium but bears theoretically unlimited risk on a naked call or substantial risk on a naked put.
- Option value has two components: intrinsic value (immediate exercise value) and time value (the premium for volatility and time remaining).
- The five key inputs to option pricing are: underlying price, strike price, time to expiry, volatility, and risk-free interest rate.
Explanation
An option is the foundational asymmetric derivative contract: the buyer pays a premium to acquire the right to participate in favorable price movements in the underlying asset, while retaining the right to walk away (by not exercising) if conditions are unfavorable. This asymmetry — unlimited upside potential capped downside for the buyer — makes options the primary instrument for hedging specific risk exposures, speculating with defined risk, and engineering complex payoff profiles.
A European call option on a stock with strike $100 and expiry in 3 months gives the holder the right to purchase the stock at $100 on the expiry date, regardless of where it trades in the market. If the stock is at $120 at expiry, the option is exercised and the intrinsic value is $20 (the stock can be purchased at $100 and immediately sold at $120). If the stock is at $90, the option expires worthless and the holder loses only the premium paid. American options differ by allowing exercise at any time before expiry, a feature that adds complexity to pricing.
Option value is the sum of intrinsic value and time value. Intrinsic value for a call = max(S − K, 0), where S is the spot price and K is the strike. Time value represents the additional premium the market pays for the possibility that the option will end up deeper in the money — driven by time remaining (more time = more chance for favorable moves) and volatility (higher volatility = greater expected range of outcomes). As expiry approaches, time value erodes — a phenomenon called time decay or theta — with the fastest erosion occurring in the final weeks before expiry.
The five primary inputs to option pricing models are the spot price of the underlying (S), the strike price (K), the time to expiration (T), the risk-free interest rate (r), and the volatility of the underlying (σ). In the Black-Scholes model, these five inputs determine a unique fair value for a European option. In practice, implied volatility — the volatility that, when plugged into Black-Scholes, produces the observed market price — is the primary trading variable in options markets, as all other inputs are directly observable.
Gamma scalping is an active strategy employed by options market makers and volatility traders who are long options: they delta-hedge their option positions by continuously rebalancing their position in the underlying, profiting from the convexity of the option (gamma) when the underlying moves. Each large move in the underlying allows the gamma scalper to buy low and sell high in the hedging process, generating realized volatility income that partially or fully offsets the theta decay cost of holding long options. Synthetic forwards — created by combining a long call and short put at the same strike — replicate the economic exposure of a forward contract without requiring delivery of the underlying, widely used in FX and commodity hedging.
Formula
Call Intrinsic Value = max(S − K, 0); Put Intrinsic Value = max(K − S, 0); Option Value = Intrinsic Value + Time Value
Example
An investor purchases a European call option on Apple (AAPL) with a strike price of $200 and expiry in 60 days. The current AAPL stock price is $195. The option's premium is $7.50 per share, or $750 for one standard contract (100 shares). If AAPL rises to $215 at expiry, the option is worth $15 intrinsically ($215 − $200), and the investor's profit = ($15 − $7.50) × 100 = $750, a 100% return on the premium invested. If AAPL falls to $185 at expiry, the option expires worthless, and the investor's loss is limited to the $750 premium paid — far less than the $1,000 loss they would have incurred holding 100 shares of stock. This demonstrates the leverage and defined-risk properties that make options attractive for speculative and hedging applications.
Related terms
Black Scholes Model Call Option Convexity Delivery Delta European Option Exchange Expiration Date Forward Contract Forward Market Gamma Gamma Scalping