# Volatility skew

**ADV-21 · Advanced Options · Core**

**Lesson question:** Which volatility are you buying or selling?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** OPT-F01, OPT-F02, OPT-F03, OPT-F04

Skew describes different implied volatilities across strikes for a given expiry. Comparing only one ATM IV misses how a multi-leg ticket prices downside and upside claims.

A higher IV at a strike is not proof that its premium is overpriced: the strike-specific risk can differ.

## Understand the mechanism

A downside put can carry different IV from an equally distant call. Delta conventions, moneyness and the underlying should match before comparison. Nominal premium can be lower even when implied volatility is higher because strike changes intrinsic and exercise probability.

A spread buys one part of the surface and sells another.

## Walk through the process

Map each leg's IV, sensitivity and liquidity. State how skew might steepen, flatten or move with spot. Revalue the full ticket under those scenarios rather than shocking every leg identically by default.

Avoid presenting past skew as an arbitrage promise or treating an IV percentile as a forecast.

## Model and implementation boundary

These are complete fictional reading examples, not live opportunities. Terminal identities assume the stated common settlement. Multi-expiry values require a surviving-leg model. Costs, assignment and financing can alter realized outcomes; a mathematical bound alone does not guarantee the same operational loss path.

## A worked example

The fictional same-expiry surface has IV 35% at strike90, 25% at100 and 23% at110. A risk reversal selling the 90 put and buying the110 call is selling and buying different points of the surface.

That can make the premium financing attractive under a hypothesis, but the short downside obligation remains. The graph contains a strike-versus-IV curve, not option prices or a predicted future move.

## Graph: Volatility skew—worked comparison

**Horizontal:** Strike (USD)  
**Vertical:** Implied volatility (%)

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/advanced-options/ADV-21.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

A trader sells the highest IV leg without considering its tail exposure or liquidity. A skew trade can lose while the average IV level barely changes.

## Check your understanding

### Does lower nominal premium mean lower implied volatility?

**Answer:** No.

**Why:** Strike and payoff affect premium as well as IV.

### What is the critical failure to avoid?

**Answer:** A trader sells the highest IV leg without considering its tail exposure or liquidity. A skew trade can lose while the average IV level barely changes.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

Return to the question: Which volatility are you buying or selling? State the observed facts, the assumptions and the failure condition separately.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [OIC Strategy Reference](https://www.optionseducation.org/strategies/all-strategies-en)

- [OCC Options Disclosure Document](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)

- [OIC Greeks](https://www.optionseducation.org/advancedconcepts/understanding-options-greeks)