Identifier: C4T3L2 | 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. Estimate delta change from gamma. 2. Apply a delta-gamma small-move approximation. 3. Stress the estimate against a large repricing.

Prerequisite: C4T3L1.

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

Gamma measures how delta changes as the underlying changes. Its units are delta per TRY of underlying price when the underlying is quoted in TRY. For a standard vanilla long option gamma is positive; the short position reverses it. Long gamma means exposure tends to become more favorable as the price moves, holding other inputs fixed. The investor pays for that curvature through premium, time effects and execution costs. Gamma is not a promise that every dynamically hedged path will earn money.

Price and return drivers

New delta estimate = delta + gamma × change in S. Per-unit option change estimate = delta × change in S + 0.5 × gamma × (change in S)^2. Multiply by signed quantity and multiplier only after matching units. The second-order term helps for small moves, but gamma itself changes with price, time and volatility. Near expiry and strike, rapidly changing gamma makes a stale estimate particularly fragile. The approximation should never replace the exact contractual expiry payoff.

Worked case

One long K100 call at premium8 has supplied delta0.50 and gamma0.04 per TRY. A TRY2 rise estimates new delta0.58. Per-unit value change is 0.50 ×2 +0.5 ×0.04 ×4 =1.08, giving TRY108 per multiplier-100 contract. Supplied full model repricing to9.10 gives TRY110; estimate error is TRY2. A TRY2 fall estimates change−1 +0.08 =−0.92, so value7.08. The asymmetry around8 demonstrates curvature rather than a constant directional exposure.

Adverse case

A TRY15 rise estimates delta1.10, already outside the usual zero-to-one vanilla call range, signaling that the local extrapolation is invalid. Its value-change estimate is7.50+4.50=12, but a supplied full reprice produces value18.20, a gain10.20 and TRY180 less than the approximate contract gain. At expiry S80,100,120, an unhedged call bought at8 has net results −820,−820,+1180 with TRY20 fees. Those exact values supersede all initial Greek estimates. Before expiry, volatility and time changes can overwhelm a gamma-only comparison.

Practical use

Define the price interval over which the estimate is used and a revaluation trigger consistent with monitoring resources. A high-gamma position can require repeated trades at widening spreads.

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 gamma to estimate how quickly a hedge can become stale and what rebalance size might be needed. Large gamma with little remaining time requires a realistic monitoring and cash budget. A short-gamma strategy tends to demand buying the hedge after rises and selling after falls; gaps and spread costs can make this expensive. Decline a tight-risk hedge plan if it assumes free continuous rebalancing. Bound the scenario, compare a full valuation, and keep delivery or assignment risk separate.

Practice and references

Exercise: one long put with delta−0.35, gamma0.03 per TRY, multiplier100. Solution: For a TRY3 fall, new delta estimate = −0.35 +0.03 ×(−3)=−0.44. Per-unit value change estimate = (−0.35) ×(−3)+0.5 ×0.03 ×9 =1.185; contract gain estimate TRY118.50. It is a local estimate at fixed time and volatility, not an expiry cash payment.

Takeaway: Gamma explains curvature and hedge drift, but large moves require fresh valuation rather than distant extrapolation. Reference links: product card, formula; glossary: Gamma; Curvature. Next: C4T3L3. 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