Identifier: C4T3L1 | 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. Convert per-unit delta into underlying units. 2. Size a local hedge with signed positions. 3. Explain the limits of a delta-neutral position.

Prerequisite: C4T2L5 and the completed earlier classes. Foundation: Stock Market School.

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

Delta measures a local change in option value for a small change in underlying price, holding other inputs fixed. A call’s standard long-position delta is positive and a put’s negative; multiplying by a short quantity reverses the sign. It is a sensitivity, not a contractual number of shares owned and not an exact exercise probability. A local hedge offsets the first-order exposure at the observation time. It does not remove volatility, jump, funding or basis risk.

Price and return drivers

Position delta in underlying units = signed contracts × multiplier × per-unit delta. For a hedge in the same underlying, take the negative of that total. If a future or a related index is used instead, its multiplier, hedge ratio and basis need separate treatment. Approximate option cash change = position delta × underlying price change. Both prices must use compatible units and currency. Recalculate after moves: a fixed hedge is no longer neutral when delta changes.

Worked case

Long 10 synthetic calls K100, premium6, multiplier100, supplied delta0.55. Position delta = 10 ×100 ×0.55 = +550 underlying units. A conceptual short550-share hedge neutralizes the current first-order exposure; it requires verified borrowing and margin, not just option premium. A TRY1 rise estimates option gain550 and hedge loss550. If the supplied full repricing is instead6.58, actual option gain is 1000 ×0.58 = TRY580, leaving TRY30 gross after the hedge. Total transaction charges40 give net −10 before borrowing, financing and actual tax.

Adverse case

For the original fixed hedge through expiry, assume entry S100, premium cash6000, total fixed fees40 and zero borrow/funding only to isolate the shape. At expiry S80,100,120, option profit is −6000,−6000,+14000; short550 shares adds +11000,0,−11000. Combined net is +4960,−6040,+2960. This three-state outcome is not flat even though initial delta was zero. Before expiry a volatility fall can reduce calls with S unchanged, while the share hedge contributes nothing. Model and executable marks must be distinguished.

Practical use

A share delta hedge needs permitted short selling, available borrow and collateral. A future hedge also needs its own multiplier and basis calculation; underlying-unit arithmetic alone grants no access.

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 delta to align a small-move risk budget, then stress full repricing and obtain borrow/funding costs. Rounding to available contract sizes creates residual exposure; a short-share hedge is not available merely because the arithmetic requests it. Decline a dynamic hedge if operational access, monitoring or cash resources are missing. If protection is the goal, a static long put may better match it even though it is not delta neutral. A delta number without its timestamp and units is incomplete.

Practice and references

Exercise: long3 puts, multiplier100, delta−0.40. Solution: Position delta = −120 units; conceptual hedge is +120 units. A TRY2 fall estimates option gain240 and hedge loss240. If the available hedge is one future with multiplier100 and delta1, long1 future leaves −20 underlying units residual delta, not neutrality. The remaining first-order gain on a TRY2 fall is TRY40 before costs and basis.

Takeaway: Position delta converts into current underlying units; local neutrality leaves changing delta, volatility and funding risk. Reference links: product card, formula; glossary: Delta; Delta hedge. Next: C4T3L2. 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: Understanding Options Greeks (retrieved 2026-10-26; Greeks and model input sensitivity). 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