Identifier: C4T3L3 | 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 quoted theta into a position cash estimate. 2. Distinguish calendar and trading-day conventions. 3. Compare frozen-input decay with a market repricing.

Prerequisite: C4T3L2.

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

Theta is the conditional sensitivity to time passing, holding other model inputs fixed. Providers can quote it per calendar day, per trading day or per year, and may use different signs for remaining-time versus elapsed-time derivatives. Read the convention before multiplying. A long standard option often has negative elapsed-time theta, but this is not a universal sign rule across deep in-the-money European options, rates and distributions. A short option’s positive theta does not insure it against a jump.

Price and return drivers

Under a supplied calendar-day convention, estimated cash change = signed contracts × multiplier × theta per option unit per day × days elapsed. This is a linear local estimate. Theta changes with moneyness and time; simply multiplying today’s number across a month can be unreliable. Weekends are already part of a model measured in calendar time; whether market quotes anticipate an event or weekend is a pricing observation, not an automatic extra deduction.

Worked case

Long4 K100 calls, premium6, multiplier100, theta−0.04 TRY per unit per calendar day. Over3 calendar days, frozen-input estimate is4 ×100 ×(−0.04) ×3 = −48. Estimated premium becomes5.88. A supplied full fixed-input reprice is5.86, giving loss56; the linear estimate understates decay by8. A hypothetical market bid6.30 after the same3 days instead gives gain120 before charges: changing underlying or volatility can more than offset time decay. The source of the mark must therefore accompany any theta explanation.

Adverse case

Expiry S90,100,120 for the original4 calls produces net −2440,−2440,+5560 with total charges40. At expiry no time value remains; multiplying original theta by90 does not generate the right endpoint. Before expiry supplied fixed-input values after3,10 and30 calendar days are5.86,5.50,4.20; corresponding position changes from6 are−56,−200,−720 before charges. These are conditional scenario outputs, not executable bids or a uniform daily coupon to the writer.

Practical use

Read the provider’s theta basis and the account’s actual cash accrual convention. Do not post estimated decay as cash income or as a guaranteed writer credit.

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 theta to budget a holding horizon, especially when an event or insurance need is delayed. Always pair it with volatility and underlying stresses. A strategy advertised as daily income may conceal negative gamma and severe tail losses. Decline a sale whose maximum obligation or cash demands exceed the budget even if current theta looks attractive. For long protection, a known premium budget can justify expected decay; the hedge’s value should be assessed against the protected exposure.

Practice and references

Exercise: short2 puts, multiplier100, provider quotes long-option theta−0.03 per calendar day. Solution: The short position’s theta is +6 TRY per day. Four elapsed days estimate +24 at frozen inputs. If the provider instead states−7.56 per unit per year using252 days, the converted daily figure is−0.03 per trading day; treating it as calendar theta would mix conventions. Actual premium must be repriced for the real observation date.

Takeaway: Theta needs a stated time and sign convention; frozen-input decay is neither actual market return nor a cash coupon. Reference links: product card, formula; glossary: Theta; Time decay. Next: C4T3L4. 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