Identifier: C4T3L4 | 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 volatility points and rate points consistently. 2. Aggregate vega and rho in cash units. 3. Identify a one-hundred-fold quotation error.

Prerequisite: C4T3L3.

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

Vega measures premium sensitivity to volatility and rho to the interest-rate input. Neither name establishes the quotation scale. “Vega0.12” may mean TRY0.12 per option unit for a one-percentage-point move in annualized volatility; a decimal-volatility derivative would instead be100 times that number. Likewise rho can be quoted per percentage point or per unit decimal rate. Store the scale, currency, model and time alongside every number before combining sensitivities.

Price and return drivers

With per-percentage-point quotations, a change from25% to28% is +3 points, not0.03 points. Estimate cash change = signed quantity × multiplier × (vega × volatility-point change + rho × rate-point change). Holding other inputs fixed is essential. For standard calls, rate increases often increase value; standard puts often have negative rho, but dividends, exercise features, underlying futures models and curve construction can change the interpretation. Rho is not the total funding cost of the customer account.

Worked case

Long5 K100 calls, premium7, multiplier100, supplied vega0.12 TRY/unit per volatility point and rho0.04 TRY/unit per rate point. Volatility25%→28% gives +3 points; rates20%→22% gives +2 points. Estimated per-unit change =0.12 ×3 +0.04 ×2 =0.44. Position estimate =TRY220. Incorrectly using0.03 and0.02 gives onlyTRY2.20, a100-fold error. This is a simultaneous first-order sensitivity estimate; it does not recompute the surface or discount curve.

Adverse case

If volatility falls5 points and rates fall2 points, estimate =500 ×(−0.60 −0.08)=−340 before fees. Supplied full repricing from7 to6.28 gives−360, showing cross-effects and changing sensitivities. At expiry S80,100,120, exact net results for the original calls are−3540,−3540,+6460 afterTRY40 charges. Expiry payoff depends on the terminal fixing, not a direct vega or rho payment. Before expiry the rate or volatility shock also can widen the spread, increasing the difference between a model mark and realizable exit cash.

Practical use

Store sensitivity currency and per-point/decimal conventions. Distinguish model rho from the account’s actual financing rate and vega from a single uniform surface shift.

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 vega and rho to expose hidden views in a directional or income strategy. Do not treat a call on a futures price as a spot call without checking model conventions. An account financed at a broker-specific rate has financing cash flows even when quoted option rho is small. Decline a comparison whose vendor scales cannot be reconciled. Stress several surface points rather than assuming every strike moves by the same volatility change.

Practice and references

Exercise: short3 puts, multiplier100, long-put vega0.15 and rho−0.03, both per percentage point. Solution: Volatility rises4 points and rates rise1 point. Long-put change estimate =0.60 −0.03 =0.57 per unit. The short position change =−3 ×100 ×0.57 =−171 TRY. Premium receipt at opening does not change this adverse mark-to-market sign.

Takeaway: Vega and rho scales must be normalized before multiplication; percentage-point and decimal errors can be one hundredfold. Reference links: product card, formula; glossary: Vega; Rho; Volatility point. Next: C4T3L5. 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