Identifier: C4T3L5 | 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. Sum signed sensitivities across legs. 2. Reconcile hedge trading and option repricing cash. 3. Stress funding and volatility risk after local hedging.

Prerequisite: C4T3L4.

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

Portfolio Greeks must share currency, underlying units, observation time and quotation scales before addition. Delta-neutral does not mean gamma-neutral, vega-neutral or cash-neutral. A dynamic hedge changes the underlying position as delta changes. It creates a path of purchases, sales, borrow obligations and transaction costs. A model that assumes continuous frictionless rebalancing should not be presented as a retail execution plan. Hedge authority and monitoring capacity are part of the decision.

Price and return drivers

Sum signed contracts × multiplier × each per-unit Greek. A local approximation combines delta × underlying move, half gamma × move squared, theta × elapsed days, vega × volatility points and rho × rate points. Do not double-count a full model reprice and its Greek explanation in the profit ledger. Profit comes from the actual cash flows and valuation changes; Greeks explain those changes approximately. Borrow charges, short-sale collateral and delivery obligations require a separate ledger.

Worked case

Conceptual synthetic hedge: long2 K100 calls at8, multiplier100, delta0.60; short120 shares atS100. Initial option cash1600 and short proceeds12000 remain subject to borrowing and collateral constraints. At S102 supplied call bid9.30, option gain260 and share hedge loss240 leave20 gross. New call delta0.70 requires short140 shares, so sell20 additional shares at102. Later S100 with supplied option bid8.50: options lose160 from9.30 and the140-share hedge gains280 from102, producing120. Total gross across both intervals is140. Charges36 on the first interval and24 on the second, plus supplied borrowing/funding30, leave50 before actual tax.

Adverse case

Before any rebalance, a jumpS100→110 with supplied call value15.50 gives option gain1500 and share loss1200, net300 gross. If a volatility fall instead leaves call value12 atS110, option gain800 and hedge loss1200 produce−400. At expiry with the original fixed120-share hedge, S80,100,120 yields gross800,−1600,0 respectively; deduct the stated total90 comparison costs to obtain710,−1690,−90. The dynamic path case has different holdings and must not be confused with this static expiry table. A margin call can arrive before an eventual profitable terminal outcome.

Practical use

Maintain a signed borrow inventory, restricted short proceeds and a rebalance cash calendar. The synthetic zero-funding isolation must be replaced by a documented real quote before implementation.

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 aggregation to decide what risk is actually retained and whether the cash plan survives the stress. A short-stock hedge needs an available borrow; its sale proceeds may be restricted. Do not assume the two quoted option marks can be realized at any size. Decline a plan that cannot finance a gap or meet its monitoring promise. Compare a simpler static spread or protection purchase when rebalance frictions dominate the estimated hedge benefit.

Practice and references

Exercise: two long calls have per-unit delta0.60 and vega0.10; one short call has delta0.30 and vega0.08, all multiplier100 and same underlying. Solution: Total delta =120 −30 =90 units; total vega =20 −8 =12 TRY per volatility point. A short90-unit underlying hedge neutralizes current delta but leaves vega+12; a five-point volatility fall estimates−60 TRY before other effects.

Takeaway: A dynamically hedged position needs a cash and borrow ledger; zero initial delta does not make the whole path neutral. Reference links: product card, formula; glossary: Portfolio Greeks; Dynamic hedge. Next: C4T4L1. 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 | Class examination