# Long and short volatility

**OPT-15 · Core Options · Core**

**Lesson question:** What is being bought when direction is uncertain?

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

Volatility strategies concern the size, path and price of movement rather than only up or down. Long options buy convexity at a cost; short options sell it while taking adverse move risk.

The strategy's name does not establish whether the volatility price is attractive.

## Understand the mechanism

A long straddle can benefit from a sufficient move either way, while a strangle pays less but generally needs more distance from its strikes. Short versions reverse cash flows and tail exposure.

For managed Delta-hedged positions, realized path and hedge costs matter; a terminal payoff alone is not the entire volatility-trading return.

## Walk through the process

State whether the thesis is a large terminal displacement, an IV increase, realized movement available to hedge or a relative-value surface move. These are different propositions.

Compare premium with a defensible scenario and costs, not with IV rank alone. A high percentile can reflect genuinely high risk.

## Contract and decision boundary

Terminal examples use simultaneous intrinsic realization of all stated legs, before unspecified costs. Actual American exercise, assignment, early liquidation and broker handling can create different interim cash needs. These fictional comparisons are education, not orders or personalized investment advice.

## A worked example

Compare a fictional 100 straddle costing 8.40 with a 95/105 strangle costing four. At expiry 106, straddle P/L is −2.40 and strangle P/L −3 per unit. At 115 they earn 6.60 and six respectively.

Lower initial cost did not make the strangle dominate every outcome. The graph shows the strangle's flat center and outer slopes; the straddle lesson provides the single-vertex comparison.

## Graph: Long and short volatility—worked comparison

**Horizontal:** Underlying at common expiry (USD)  
**Vertical:** Strangle 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/options-strategies/OPT-15.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

Assuming all long-volatility trades benefit from any small move ignores the premium and strikes. Treating a high win rate in short vol as safety ignores severity.

## Check your understanding

### What is the 95/105 strangle's terminal loss at 106 with total debit four?

**Answer:** 300 per standard pair.

**Why:** One call intrinsic minus four paid.

### What is the critical failure to avoid?

**Answer:** Assuming all long-volatility trades benefit from any small move ignores the premium and strikes. Treating a high win rate in short vol as safety ignores severity.

**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 is being bought when direction is uncertain? 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.

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

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