Who this chapter is for — Readers encountering calls and puts for the first time, as well as professionals who need to make their reading of an option chain, volatility surface, Greeks or multi-leg payoff reproducible. The path begins with the contract and advances without turning a measure into a trading signal.
Options separate dimensions that can appear joined in a linear instrument: direction, time, volatility, convexity, financing, dividends, exercise and settlement. A terminal chart can be correct yet insufficient; an implied volatility can be calculated precisely while still depending on the model and the selected quote; a familiar strategy can change its risk if one leg is closed or assigned.
This hub organises the classical, publicly verifiable knowledge of options and volatility. It contains no signals, recommendations or rules from the Emiciclo Method. That method can later be added as a separate layer. The first task is to establish a historical and technical foundation that remains intelligible without proprietary interpretations.
Chapter map
| Node | The right question | Shortcut to avoid |
|---|---|---|
| What rights, obligations and specifications does the contract contain? | “a call is always bullish” | |
| Which dispersion is being measured, from which data and by which method? | confusing magnitude with direction | |
| What is a tradable quote and what is a value produced by a model? | treating the midpoint as a certain price | |
| To which timestamp, expiry, strike and quote side does the figure belong? | reading a table as a signal | |
| Does the number come from option prices or from observed returns? | calling IV a certain forecast | |
| How does one consistent coordinate vary across expiries at the same instant? | confusing it with a historical series | |
| How does IV vary by strike or moneyness and expiry? | confusing it with statistical skewness of returns | |
| What relation connects calls, puts, spot or forward and the value of the strike? | applying the equality without its conditions | |
| Who can exercise, who can be assigned and what is settled? | assuming identical rules for every contract | |
| What is the signed sum of every leg, quantity and premium? | believing that the strategy name guarantees limited risk | |
| What is the local slope with respect to the underlying? | using it as a universal probability | |
| How does delta change when the underlying changes? | treating it as constant | |
| How does value respond to one point of implied volatility? | adding incompatible scales or nodes | |
| How does theoretical value change with time while other inputs remain fixed? | calling it a certain daily loss |
1. Contract first, chart second
The Options entry distinguishes calls and puts, buyers and sellers, strike, premium, expiry, multiplier, exercise style and settlement. These are contractual coordinates, not administrative details. An option on a stock, index or futures contract can create a different deliverable; “one contract represents 100 units” is common in some markets, not universal.
The payoff of a call at expiry is max(S_T − K, 0), while that of a put is
max(K − S_T, 0). The buyer’s result subtracts the premium and costs. Before
expiry, however, the price also contains time and other variables: the
terminal profile is not the mark-to-market path.
The Option premium and valuation guide separates intrinsic value, time component, bid-ask quote, theoretical value and model assumptions. A break-even derived from the payoff applies at expiry and before the stated costs. It is not the probability of profit and does not prevent the position from being closed earlier at a gain or loss.
2. Reading a chain without inventing liquidity
An option chain arranges expiries and strikes and may display bid, ask, last, volume, open interest, implied volatility and Greeks. These fields do not share the same timestamp or meaning. The last trade may be stale, the midpoint may not be executable, volume is flow during the measurement period, and open interest is a stock of outstanding contracts under the applicable accounting rules.
A professional reading preserves the exact contract, quote side, time, currency, multiplier and conventions. Comparing a call bid with a put ask, or two IV figures calculated from different inputs, can manufacture an artificial difference. The chain is a market dataset, not embedded advice.
3. From observed volatility to implied volatility
Realized volatility starts from returns and requires a frequency, window, estimator and annualisation convention. Implied volatility travels in the opposite direction: given an option price and a model with the remaining inputs, one searches for the volatility value that makes the theoretical price consistent with that option price. IV is therefore not raw data observed in the same way as price, and it is not a certain forecast of future realized volatility.
Bid, midpoint and ask can produce different IV figures. Model, rates, dividends, forward, exercise style and day-count convention are part of the result. Comparing implied and realized volatility can be informative, but it does not determine P&L on its own: path, hedging, smile, jumps, costs and execution all matter.
The volatility term structure compares expiries at the same instant while keeping a coordinate such as moneyness or delta consistent. The surface adds the strike or moneyness axis. A section across strikes is a smile or skew; a section across expiries is a term structure. Neither is a time series or a directional verdict.
4. Structural relations and operational risk
Put-call parity links the prices of European calls and puts with the same strike and expiry to the underlying or forward and the present value of the strike. Dividends, financing, settlement, borrow, costs and American exercise change its application. A theoretical relation can diagnose consistency and construct equivalences, but it does not promise an executable arbitrage.
The Exercise, assignment and settlement entry follows a position from trading through close-out, exercise or expiry. European style limits exercise, not the ability to close the position earlier in the market. Automatic-exercise thresholds, cut-offs, contrary instructions and broker procedures depend on the relevant framework. An assigned writer may receive an underlying position, cash or a futures position and may need capital earlier than the final payoff suggests.
In multi-leg option strategies, the profile is the signed sum of legs, quantities, premiums, the underlying and any financing. Spread, condor and straddle are useful names, not certificates of limited risk. Legging, partial fills, assignment of only one leg, liquidity and margin can transform the exposure.
5. The four sensitivities already verified
Greeks describe local responses within a model:
- delta with respect to the underlying;
- gamma as curvature with respect to the underlying and as the change in delta;
- vega with respect to implied volatility, with a per-point or per-unit scale that must be stated;
- theta with respect to the passage of time, with sign and unit made explicit.
A local approximation can be written as:
ΔV ≈ Delta·ΔS + ½·Gamma·(ΔS)² + Vega·Δσ + Theta·ΔtThis is not an identity for large shocks. Greeks change along the path, smile and expiry move, cross terms exist, and a model residual remains. Material decisions require joint repricing and scenarios, not merely a sum of frozen sensitivities.
Three reading paths
First encounter with options
Volatility and pricing
Position risk
Sources
- The Options Clearing Corporation, Characteristics and Risks of Standardized Options — official document on contracts, exercise, assignment, settlement and the risks of combinations in the United States market.
- The Options Industry Council, What Is an Option? and Options Pricing — contractual foundations and components of the premium.
- The Options Industry Council, Volatility & the Greeks and Put/Call Parity — volatility, sensitivities and price relations.
- Financial Industry Regulatory Authority, Trading Options: Understanding Assignment — mechanics and assignment risk in the United States framework.
- Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973 — historical reference for the model, read together with its assumptions and subsequent developments.
- CME Group, Implied Volatility — the relation between option prices, implied volatility and skew.