# Think in risk shapes

**ADV-01 · Advanced Options · Core**

**Lesson question:** What exposure does the combination actually create?

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

Advanced options begins with decomposing risk, not memorizing more names. A combination can be directional, convex, range-focused or relative-value, and its current sensitivities can change with spot, time and IV.

A strategy nickname is a starting description, not a complete specification.

## Understand the mechanism

A long vanilla option has positive Gamma and Vega in smooth European BSM, but its Theta is not universally negative in every state. Short quantities reverse sensitivities. Multi-leg positions can change their net Greek signs across states.

Terminal payoff and pre-expiry value are distinct. A calendar cannot be reduced to a single fixed terminal V by pretending both legs expire together.

## Walk through the process

Read every signed leg and the cash flow. Identify dominant risks now and in adverse states. Test flat spot with time passing, a directional jump and an IV-surface change.

Progress means explaining why a chosen exposure fits the thesis, not increasing complexity or leverage.

## 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

A fictional 100/105 bull-call vertical pays two points. Its terminal P/L is −200 below 100, rises through zero at 102 and caps at +300 above 105 for one standard spread.

The short call is what limits participation above 105. Removing it does not 'improve' the same trade for free: it changes cost and risk. The graph shows the full combination rather than one leg alone.

## Graph: Think in risk shapes—worked comparison

**Horizontal:** Underlying at common expiry (USD)  
**Vertical:** Vertical terminal P/L (USD)

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-01.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

A trader assigns fixed Greeks to a strategy by name or treats a cheaper structure as automatically better. Its risk shape can differ fundamentally.

## Check your understanding

### What causes the bull-call spread's upside cap?

**Answer:** The higher-strike short call.

**Why:** The sold option finances part of the cost and offsets later upside.

### What is the critical failure to avoid?

**Answer:** A trader assigns fixed Greeks to a strategy by name or treats a cheaper structure as automatically better. Its risk shape can differ fundamentally.

**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: What exposure does the combination actually create? 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)