Identifier: C4T2L2 | 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. Check an option against defensible price bounds. 2. Reconcile matched European call and put values. 3. Separate an apparent violation from executable arbitrage.

Prerequisite: C4T2L1.

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 no-arbitrage relationship compares portfolios with the same future cash flows. For European calls and puts on one non-dividend-paying asset, matched strike, expiry and settlement, call plus present value of strike replicates put plus underlying. The cash account is a real financing leg, not a notation to omit. A share with distributions or a mismatched contract requires an adjustment. American early exercise changes the equalities and constraints; the simple European relation cannot be applied mechanically.

Price and return drivers

With supplied discount factor D, C − P = S − K×D. For nonnegative rates and no dividends, max(S − K×D,0) ≤ C ≤ S; max(K×D − S,0) ≤ P ≤ K×D. These are model-independent bounds within the assumptions. They are not assertions that a European call always exceeds immediate spot intrinsic under distributions. The parity check must use contemporaneous quotes and the correct delivery terms; a theoretical midpoint discrepancy is not a realizable cash profit.

Worked case

Synthetic inputs: S100, K100, one-year expiry, discount factor 0.95 and put midpoint 7. Present strike value is TRY 95 per unit, so call midpoint consistent with parity is 7 + 100 − 95 = 12. Call lower bound is 5 and upper bound 100; put bounds are 0 and 95. At expiry S70, S100 and S140, call plus cash pays 100,100,140; put plus stock also pays 100,100,140. The common portfolio payoff is max(S,100), independent of the initial premium decomposition.

Adverse case

Suppose the call midpoint is 13 rather than 12. The apparent excess is 1 per unit, or TRY 100 for one multiplier-100 package. Executing at the correct quote sides costs a supplied TRY 60 across the legs; borrow and financing cost another TRY 70. Net is 100 − 60 − 70 = −30 before tax, so the apparent trade should be declined. Before expiry, mismatched funding rates or dividend assumptions can make marks diverge; expiry payoff identity alone does not ensure that every leg can be funded or closed together.

Practical use

Check simultaneous executable quote sides, distributions, stock borrowing and the cash financing leg. A parity diagnostic alone does not authorize an implementable arbitrage.

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 parity as a data-quality and funding diagnostic. A discrepancy can flag a stale option, wrong unit scale, incorrect dividend date or adjustment. To propose arbitrage, document executable legs, stock borrow, financing, fees, tax, settlement and simultaneous execution. If any leg is inaccessible, the parity number remains an analytic comparison. A bound is only as valid as its stated assumptions and does not guarantee liquidity at that value.

Practice and references

Exercise: S80, K90, supplied discount factor 0.96, European put premium 12, no dividends. Solution: Present strike = 86.40; parity call = 80 + 12 − 86.40 = 5.60. Call lower bound is zero and put lower bound 6.40. A quoted call of 5.60 passes these tests; passing a bound does not establish that it is attractive or executable.

Takeaway: Parity aligns matched cash flows including strike financing; a midpoint discrepancy can disappear after executable costs. Reference links: product card, formula; glossary: Put call parity; No arbitrage bound. Next: C4T2L3. Topic test.

Sources: Borsa Istanbul: Settlement Method (retrieved 2026-10-26; Settlement by contract family). Options Industry Council: Put/Call Parity (retrieved 2026-10-26; Parity formula, financing, dividends and implementation restrictions). 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.

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