Identifier: C4T2L5 | Revision: 2026-10-26 | Planned study: 10–15 minutes, excluding extended practice.

Decision and objectives

Choose whether the method addresses this lesson’s task before placing an order. Objectives: 1. Compare implied volatility on matched units. 2. Distinguish strike skew from expiry term structure. 3. Stress event resolution separately from direction.

Prerequisite: C4T2L4.

All numbers, quotes, contract terms and dates in the case are hypothetical teaching assumptions, not a listed series or offer. Unless varied below, options are European, expire together in 90 calendar days, are cash settled in TRY, and use 100 underlying units per contract. Premiums are TRY per underlying unit, paid at entry; signed quantities identify long (+) and short (−) legs. Assume no distributions and zero financing for the isolated payoff, no holiday adjustment, and final cash on the next business day. Actual tax is excluded, not assumed zero.

Mechanics

A volatility surface arranges model-implied inputs by strike and expiry. Skew is variation across strikes at one expiry. Term structure is variation across expiries for a comparable moneyness definition. Compare like with like: a deep put and an at-the-money call may have different sensitivities and spreads. A high implied input around an announcement can reflect the price of jump exposure; it does not tell the announcement’s direction. The option’s absolute premium also depends on remaining time and moneyness.

Price and return drivers

Volatility × square root of time is a rough one-standard-deviation move scale under a diffusion approximation. With annual volatility in decimals and time in years, it yields a fractional move. It is not a guaranteed range, especially around scheduled jumps. Compare total variance volatility squared × time when isolating event versus non-event periods, rather than simply subtracting annualized percentages. A short expiry can carry higher annualized volatility while having lower total premium than a longer expiry.

Worked case

Original hypothetical input surface: 30-day expiry put K90 implied35%, at-the-money K100 implied30%, call K110 implied27%; 90-day at-the-money input24%. This is downside skew and an elevated short-end input. At S100 the 30-day move scale is 100 × 0.30 × sqrt(30/365) = 8.6007 TRY; the 90-day scale is 100 × 0.24 × sqrt(90/365) = 11.9175. Higher annualized short volatility does not imply the larger full-horizon scale. These are diagnostic scales, not calibrated probability intervals.

Adverse case

A synthetic one-contract long K100 call bought at premium5 before an event has a supplied post-event bid4 at S103: net loss = 100 × (4 − 5) −20 = −120. The event resolved favorably in direction but removed priced uncertainty. Expiry S90,100,120 yields net −520,−520,+1480. For a pre-expiry event stress, supplied bids2,4,8 imply net −320,−120,+280. These are scenario quotes, not deterministic implications of a volatility point change, and they keep the expiry and interim questions separate.

Practical use

Match strike moneyness and expiry conventions across the surface, identify the event date, and check whether the protection survives through it.

For any actual domestic implementation, verify the exact issue/contract, authorized intermediary, account permission and executable size. Include spread, commissions, passed-through fees, funding/borrow, custody and exercise/exit costs without double-counting embedded charges. Recheck income year, residency/status, issue/acquisition dates and effective tax law; all case results remain before actual tax.

Decision boundaries

Use the surface to question why one strike or horizon is expensive and whether the event belongs inside the protection period. Do not subtract 30% and24% and call6% the event move. Normalize time, forward moneyness, model and quote timestamps. Decline a supposed relative-value trade when different expiries leave an uncovered event or the quote data cannot be synchronized. Residual skew, jump and spread risk can dominate a directional forecast.

Practice and references

Exercise: annualized input40%, S200, 7 calendar days. Solution: Move scale = 200 ×0.40 ×sqrt(7/365) = TRY11.0788. An actual jump of TRY20 is possible; the scale is not a barrier. For a 28-day input20%, the same calculation also gives TRY11.0788, illustrating why annualized percentages alone cannot rank total uncertainty.

Takeaway: Annualized volatility, horizon and event timing must be read together; a favorable event direction can still lose premium. Reference links: product card, formula; glossary: Volatility skew; Term structure; Event risk. Next: C4T3L1. Topic test.

Sources: Borsa Istanbul: Options (retrieved 2026-10-26; General information and basic concepts). Borsa Istanbul: Settlement Method (retrieved 2026-10-26; Settlement by contract family). Options Industry Council: Black-Scholes Formula (retrieved 2026-10-26; Inputs and pricing-model limitations). GIB: Provisional Article67 Guide for Individuals (retrieved 2026-10-26; Sections1,3–9 and19; publication introduction). Revision 2026-10-26; recheck changing terms before publication.

Shared reference guide | Class examination