Option book construction from implied volatility, historical volatility and premium

Three inputs for construction

Options can be assembled as a book rather than as a single isolated contract. The archive workflow supplies three measurements that sit on that book: a backward-looking volatility reading, a volatility recovered from live option prices, and the cash that changes hands as premium.

Editorial reading: those three measurements can be treated as a design problem. Historical volatility states the regime the path has already delivered. Implied volatility states the regime the market is pricing. Net premium is the cash accepted or paid to sit in the gap between those two regimes.

Historical volatility as the delivered regime

Historical volatility describes how much a contract price has already fluctuated. It is usually estimated as the standard deviation of price changes over a selected period.

A companion volatility reading describes a stock’s tendency to move from daily price history over the prior 12 months. Both readings look backward. They describe delivered movement, not the volatility recovered from an option’s market price.

Implied volatility as the priced regime

Implied volatility is the volatility recovered from an option’s actual market price by feeding that price into a pricing model. In the terminology used here, it is the volatility recovered from an option’s live market price by inserting that price into a pricing model.

If an option’s market price rises while the underlying price is unchanged, implied volatility is treated as having risen. Editorial reading: the priced regime can therefore move even when the delivered path has not.

Premium as the cash in the gap

Premium is the cash a buyer pays a writer to grant an option contract. It is the cash accepted or paid to sit with the rights in that contract.

A credit spread is the value gap when the sold option is worth more than the purchased option. A debit spread is the reverse gap, when the purchased option is worth more than the sold one.

Editorial reading: the sign of that net premium is how the book records whether cash was taken in or paid out to occupy the gap between priced and delivered volatility.

Structures that express the gap

A straddle uses equal puts and calls with the same strike and expiration. A strangle uses the same expiration but different strikes, typically a lower put strike and a higher call strike.

Calendar or time spreads are built to capture differences in time value across expirations. Vertical spreads buy and sell the same expiration at different strikes. Credit and debit versions of those two-option structures follow from which contract is worth more.

Sensitivities that keep the book aligned

Delta is the option-price change associated with a one-dollar move in the underlying. A delta-hedged book offsets that exposure with an opposite underlying position of equal magnitude. The same idea is called delta-neutral when the mix of options and the underlying is sized so the book is relatively insensitive to small price moves.

Vega is the option-price change associated with a change in volatility. Zeta is the percentage option-price change per one-percent change in implied volatility. Editorial reading: vega and zeta describe how the book responds if the priced regime moves after the structure is on.