Pricing and Greeks

An option's price depends on the underlying price, strike, time to expiry, volatility and other inputs such as interest rates and dividends.

Intrinsic and time value

Intrinsic value is the positive difference between underlying and strike for a call, or strike and underlying for a put. The remaining premium is commonly called time value. See OIC's pricing guide.

Volatility

Historical volatility measures past price variation. Implied volatility is the volatility input that makes a pricing model match the observed option price. It is model-dependent, not a guaranteed forecast.

For standard calls and puts, higher volatility generally increases model value when other inputs stay fixed. Different strikes and expiries can imply different volatilities. See OIC on volatility.

The Greeks

Greeks describe local sensitivities, holding other inputs fixed:

Their units and quoting conventions matter. They change as the market and time change. See OIC's Greeks guide.

Hedging

A delta hedge offsets an estimate of exposure to small underlying price moves. It does not remove gamma, volatility, model or execution risk. The hedge may need adjusting as delta changes. See OIC on delta.

Reading a volatility surface

A volatility surface describes implied volatility across strikes and expiries. A smile or skew describes variation across strikes; term structure describes variation across expiries.

A single volatility input loses this information. Repricing a position after a move may require assumptions about how the whole surface changes, not just an increase or decrease in one number.

Position Greeks

Scale each contract's Greeks by its multiplier and signed quantity before adding them. A portfolio's delta is an exposure under the chosen conventions, not simply the number of options held.

For standard vanilla options, a long option is usually positive gamma and positive vega. Selling the same option reverses those sensitivities. Theta conventions and exceptions matter, so read the calculation's units and sign definition.

Limits of a local estimate

Delta is a first-order approximation. Gamma describes how delta changes, but a large move, a volatility change or approaching expiry can still make a local estimate inaccurate.

Use full repricing for scenarios where those effects matter. Keep the model inputs and market data consistent across the portfolio. A precise calculation with stale inputs can still give a poor estimate.