CIRO Derivatives: Element 4 — Derivative Pricing

Try 10 focused CIRO Derivatives questions on Element 4 — Derivative Pricing, with answers and explanations, then continue with Securities Prep.

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Sample questions

These questions are original Securities Prep practice items aligned to this topic area. They are designed for self-assessment and are not official exam questions.

Question 1

Topic: Element 4 — Derivative Pricing

An Approved Person is discussing a near-the-money call option on the Bourse de Montreal with a retail client who has limited derivatives experience. The client expects only a small rise in the underlying over the next month, but the option expires in five days. Which action best aligns with CIRO standards and correctly applies theta?

• A. Highlight leverage now and review time decay after execution.
• B. Focus on delta because theta matters only if the option finishes in-the-money.
• C. Enter the order because listed options are standardized products.
• D. Explain the call has negative theta and confirm the trade remains suitable.

Best answer: D

What this tests: Element 4 — Derivative Pricing

Explanation: Theta measures an option’s sensitivity to the passage of time. For a near-the-money long call with only five days left, time decay can be rapid, so the Approved Person should explain that risk clearly and confirm the trade is still suitable before proceeding.

Theta is the Greek that estimates how much an option’s value tends to decline as time passes, all else equal. A long call typically has negative theta, and that effect is often most important when expiry is close. Here, the client’s market view is modest and extends over a month, but the option expires in five days, so the premium could erode before the expected move occurs.

Under CIRO’s fair-dealing, know-your-product, and suitability expectations, the Approved Person should disclose that material risk in plain language and reassess whether the trade fits the client’s experience, risk tolerance, and time horizon. A response that treats standardization as a substitute for disclosure, or that postpones the discussion until after execution, does not meet that standard.

• Proceeding just because the option is standardized ignores the need to explain material risks and assess suitability when advising a retail client.
• The idea that theta matters only if the option finishes in-the-money is incorrect; time decay affects option value before expiry and can be severe near expiry.
• Discussing leverage first and delaying the time-decay discussion until after execution fails timely disclosure and fair-dealing expectations.

This best combines accurate disclosure of time decay with the duty to ensure the strategy still fits the client’s objectives, risk tolerance, and experience.

Question 2

Topic: Element 4 — Derivative Pricing

A client is comparing a Bourse de Montreal S&P/TSX 60 index futures contract and an at-the-money call option on the same index, both with the same expiry. If the index rises today and interest rates, expected dividends, volatility, and time to expiry are unchanged, which statement best describes the pricing impact?

• A. Both rise; the futures tracks the index more directly.
• B. The call is unchanged until expiry.
• C. Both rise; the call tracks the index more directly.
• D. The futures falls because a higher index lowers fair value.

Best answer: A

What this tests: Element 4 — Derivative Pricing

Explanation: When the underlying index rises, both the futures contract and the call option should gain value. The decisive difference is sensitivity: futures are near-linear exposure to the underlying, while a call option’s premium rises too but usually less directly because it depends on delta and time value.

The core concept is how directly each derivative responds to the underlying. A futures contract’s fair value is anchored to the spot index plus carrying effects, so if the index rises and the other inputs stay fixed, the futures price also rises almost point-for-point. A call option also becomes more valuable when the underlying rises because its intrinsic value improves and the chance of finishing in the money increases. However, an at-the-money call usually has a positive delta below 1, so its premium does not normally move one-for-one with the index.

The key comparison is linear exposure versus option sensitivity. Futures are the more direct pricing response to the underlying move, while calls have upside sensitivity but not the same point-for-point behavior.

• Call more direct confuses positive delta with linear exposure; an at-the-money call is usually less sensitive than a futures contract.
• Futures falls reverses the spot-futures relationship; with carry inputs unchanged, a higher index lifts futures fair value.
• Unchanged until expiry ignores that option premiums reprice continuously before expiry as the underlying moves.

With other inputs fixed, a futures price follows the underlying almost one-for-one, while an at-the-money call also rises but usually by less than the full index move.

Question 3

Topic: Element 4 — Derivative Pricing

A client is considering a listed option on a non-dividend-paying Canadian stock traded on the Bourse de Montreal. Assume the stock price is unchanged while implied volatility and interest rates both rise. Which position would generally gain value from both changes?

• A. Short put option
• B. Short call option
• C. Long put option
• D. Long call option

Best answer: D

What this tests: Element 4 — Derivative Pricing

Explanation: Vega measures sensitivity to implied volatility, and long options have positive vega. Rho measures sensitivity to interest rates; for equity options on a non-dividend-paying stock, calls generally have positive rho while puts generally have negative rho, so only the long call benefits from both moves.

Vega shows how much an option’s value changes when implied volatility changes. Long calls and long puts both have positive vega, while short options have negative vega. Rho shows how much an option’s value changes when interest rates change. For equity options on a non-dividend-paying stock, call rho is generally positive and put rho is generally negative because higher rates make paying the strike later relatively more attractive for calls and less attractive for puts.

With the stock price held constant, higher implied volatility helps long options, but higher interest rates help calls and hurt puts. That means the only position that benefits from both effects at the same time is the long call. The closest distractor is the long put, which shares positive vega but not positive rho.

• Long put trap benefits from higher implied volatility, but rising rates generally reduce a put’s value.
• Short call mismatch has negative vega and negative rho, so both changes work against the position.
• Short put mismatch benefits from higher rates, but higher implied volatility hurts a short option position.

A long call has positive vega and, for an equity option on a non-dividend-paying stock, positive rho.

Question 4

Topic: Element 4 — Derivative Pricing

Using the convention basis = spot - futures, an S&P/TSX 60 futures contract on the Bourse de Montreal trades at 1,330. The spot index is 1,323, and fair value based on carrying costs is 1,326. Which interpretation best matches this pricing scenario?

• A. The basis is +4, and convergence means the premium should widen.
• B. The basis is +7, and cash-and-carry means buy the basket and sell the futures.
• C. The basis is -7, and reverse cash-and-carry means sell the basket and buy the futures.
• D. The basis is -7, and cash-and-carry means buy the basket and sell the futures.

Best answer: D

What this tests: Element 4 — Derivative Pricing

Explanation: With basis defined as spot minus futures, the basis is -7. The futures price is also 4 points above fair value, so the matching arbitrage is cash-and-carry: buy the underlying basket and sell the futures.

Start with the stated basis convention: spot minus futures. That gives 1,323 - 1,330 = -7, so the basis is negative because the futures price is above the spot index. Next compare the actual futures price with fair value. Since 1,330 is above the fair value of 1,326, the futures contract is rich relative to carry-adjusted pricing. In that situation, a cash-and-carry arbitrageur would buy the underlying basket in the cash market and sell the overpriced futures contract.

As expiry approaches, futures and spot should converge, so the gap tends to narrow rather than widen. The main traps are reversing the basis sign, confusing cash-and-carry with reverse cash-and-carry, and mistaking the 4-point mispricing to fair value for the basis.

• The statement using +7 reverses the stated basis convention; spot minus futures is negative when futures exceed spot.
• The statement using reverse cash-and-carry flips the trade direction; that strategy fits when futures are cheap relative to fair value.
• The statement using +4 confuses mispricing versus fair value with basis and also gets convergence backward, since the gap should narrow into expiry.

Basis is 1,323 - 1,330 = -7, and because the futures is above fair value 1,326, the arbitrage is to buy the underlying basket and sell the futures.

Question 5

Topic: Element 4 — Derivative Pricing

An options trader at a Canadian Investment Dealer is short a near-the-money listed call and has delta-hedged the position with shares. Because expiry is very close, the option has high gamma. If the underlying share price rises sharply and implied volatility is unchanged, what is the most likely outcome?

• A. The position turns short delta, requiring share purchases.
• B. The position turns long delta, requiring share sales.
• C. Re-hedging is unnecessary unless volatility also rises.
• D. The hedge stays near neutral because gamma measures time decay.

Best answer: A

What this tests: Element 4 — Derivative Pricing

Explanation: Gamma measures how quickly delta changes when the underlying price moves. A short near-the-money call close to expiry has large negative gamma, so a sharp rise in the stock makes the position more short delta and creates a need to buy shares to re-hedge.

Gamma is the rate of change of an option’s delta as the underlying price changes. Near-the-money options close to expiry typically have the highest gamma, so their delta can change quickly after even a small price move. Because the trader is short the call, the position has negative gamma. When the stock rises, the call’s delta increases; from the short seller’s perspective, that means the position becomes more negative delta. A hedge that was neutral at the start therefore drifts short delta, and the trader must usually buy shares to get back to neutral. The key application of gamma is hedge stability: high-gamma short-option positions need more frequent adjustment, especially in fast markets.

• Wrong sign The idea that the hedge turns long delta reverses the effect of a short-gamma position after an upward move.
• Theta confusion Time decay is measured by theta, not gamma; gamma tells you how fast delta changes.
• Volatility not required A price move alone can force re-hedging when gamma is high, even if implied volatility is unchanged.

Short call positions have negative gamma, so an upward move makes the position more negative delta and the hedge must be restored by buying shares.

Question 6

Topic: Element 4 — Derivative Pricing

Which statement best describes convergence between a futures price and the cash price of its underlying as expiry approaches?

• A. Only physically delivered futures can converge with the cash market at expiry.
• B. Futures and cash prices move toward each other, the basis approaches zero, and arbitrage helps enforce fair value.
• C. The futures price moves back toward the original contract price agreed when the trade was opened.
• D. The basis widens because carrying costs keep building over the contract term.

Best answer: B

What this tests: Element 4 — Derivative Pricing

Explanation: Convergence is the tendency for futures and cash prices to move toward the same value as expiry nears. As that happens, the basis narrows toward zero, and arbitrage such as cash-and-carry or reverse cash-and-carry helps keep the relationship close to fair value.

Convergence is a core futures-pricing concept. As expiry gets closer, there is less time for financing, storage, income effects, or other carrying-cost differences to separate the futures price from the cash price. The basis, meaning the difference between cash and futures prices, therefore narrows and should be close to zero at expiry, aside from normal market frictions.

Arbitrage helps enforce this relationship. If futures are too expensive relative to cash and carrying costs, a trader can use cash-and-carry arbitrage by buying the underlying and selling the futures. If futures are too cheap, reverse cash-and-carry can push prices the other way. The key point is that convergence compares the current futures price with the current cash price, not the original trade price or the delivery method.

• Wider basis confuses cost of carry with convergence; near expiry, the cash-futures difference normally narrows rather than widens.
• Original trade price is irrelevant because convergence compares the current futures price with the current cash price.
• Physical delivery only is incorrect because cash-settled futures also align with the underlying cash market at final settlement.

Convergence means the cash-futures price difference narrows toward zero as expiry approaches, with arbitrage helping keep pricing near fair value.

Question 7

Topic: Element 4 — Derivative Pricing

An Approved Person is reviewing a European option pair on a Canadian equity before discussing a hedge with a client. The stock is trading at $50.00. A call with strike $52 and the same expiry is trading at $4.80. There are no dividends before expiry, and the present value of the strike is $51.60. To meet CIRO fair-dealing and know-your-product expectations, which response best estimates the corresponding put’s fair value?

• A. Estimate the put near $2.00 using intrinsic value only.
• B. Estimate the put near $4.80 because premiums should match.
• C. Estimate the put near $6.40 using put-call parity.
• D. Estimate the put near $6.80 using the full strike price.

Best answer: C

What this tests: Element 4 — Derivative Pricing

Explanation: Fair dealing and know-your-product require a reasonable pricing check before discussing the trade with the client. With no dividends and matching European options, put-call parity gives \(P = C + PV(K) - S = 4.80 + 51.60 - 50.00 = 6.40\), so the put’s fair-value estimate is about $6.40.

Put-call parity links a call, a put, the underlying stock, and the present value of the strike for European options with the same strike and expiry. In this no-dividend setting, an Approved Person acting fairly should use that relationship to sanity-check price before discussing strategy or suitability with the client.

• Start with \(P = C + PV(K) - S\).
• Substitute the facts: \(4.80 + 51.60 - 50.00\).
• The result is \(6.40\).

Using intrinsic value alone or using the full strike instead of its present value would misstate fair value.

• Intrinsic only gives about $2.00, but parity requires both intrinsic and time value.
• Equal premiums ignores the stock price and present value of the strike, so matching calls and puts are not simply equal.
• Full strike amount overstates the put because parity uses the present value of the strike, not the undiscounted $52.

Put-call parity gives the put a fair value of $6.40 because \(P = C + PV(K) - S = 4.80 + 51.60 - 50.00 = 6.40\).

Question 8

Topic: Element 4 — Derivative Pricing

A client with an approved derivatives account owns 2,000 shares of ABC at $50 and asks whether listed calls could provide roughly similar immediate upside exposure with less cash. Each call contract covers 100 shares and has a delta of 0.50. Which response by the Approved Person best aligns with CIRO standards?

• A. Place 40 call contracts first, then provide delta and risk disclosure on the confirmation.
• B. Recommend 40 call contracts and describe delta as fixed until expiry.
• C. Recommend 20 call contracts because options are leveraged and delta need not be considered.
• D. Use delta to estimate about 40 call contracts, explain it can change, and complete suitability review before trading.

Best answer: D

What this tests: Element 4 — Derivative Pricing

Explanation: Delta is both an option price sensitivity measure and a practical way to estimate share-equivalent exposure. A 0.50 delta call on 100 shares gives about 50 delta-equivalent shares, so 40 contracts approximate 2,000 shares. That explanation must still be paired with pre-trade suitability review, disclosure, and documentation.

Delta measures the approximate change in an option’s premium for a $1 move in the underlying, and it is also used as a hedge-ratio estimate. Here, each call contract covers 100 shares, so a 0.50 delta call represents about 50 delta-equivalent shares. To approximate the client’s current directional exposure of 2,000 shares, the Approved Person would start with about 40 contracts. Under CIRO fair-dealing and suitability expectations, that discussion must be paired with proper risk disclosure and documentation before any order is accepted, because listed calls add leverage and can still lose their full premium. The key point is to explain delta as a current estimate that can change with price, time, and volatility, not as a promise.

• Leverage shortcut fails because leverage does not replace using delta to size exposure or completing suitability analysis.
• Fixed delta fails because delta is only a current estimate and can change before expiry.
• Late disclosure fails because material risks and suitability must be addressed before the order is accepted.

It correctly applies delta as a current exposure estimate and adds the required pre-trade suitability, disclosure, and documentation steps.

Question 9

Topic: Element 4 — Derivative Pricing

A pricing approach divides the life of an option into a series of time steps, models possible up and down moves in the underlying, and can test whether early exercise is optimal at each step. Which pricing model matches this feature?

• A. Put-call parity relationship
• B. Binomial option-pricing model
• C. Black-Scholes option-pricing model
• D. Intrinsic value calculation

Best answer: B

What this tests: Element 4 — Derivative Pricing

Explanation: That feature describes the binomial model. It values an option with a discrete price tree and works backward through the nodes, which lets the analyst compare holding versus early exercise during the option’s life.

The key distinction is the model structure. A binomial model divides time to expiry into small intervals and maps possible up and down moves in the underlying asset. The option is then valued by working backward through the tree, so the model can test at each node whether early exercise has value. That makes it especially useful for American-style options in foundational exam questions. By contrast, the basic Black-Scholes treatment assumes continuous price movement and is mainly associated with European-style options, where exercise is only at expiry. Put-call parity is a pricing relationship, and intrinsic value is only one component of an option’s value. The tree-and-node clue is what identifies the binomial model.

• Black-Scholes mismatch because the classic exam treatment does not use a discrete tree with node-by-node exercise checks.
• Parity mismatch because put-call parity links option prices algebraically; it is not a step-by-step valuation model.
• Intrinsic value mismatch because intrinsic value measures immediate exercise value only and ignores time value.

It uses a price tree over discrete time steps, so early-exercise decisions can be checked at each node.

Question 10

Topic: Element 4 — Derivative Pricing

A derivatives trader at a Canadian Investment Dealer is checking the fair value of a 6-month futures contract on Maple Energy shares. The options are European-style, all amounts are in CAD, no dividends are expected before expiry, and assume the fair value of the futures price equals the fair value of the forward price.

Exhibit: September pricing

Using put-call parity, which futures price is supported by the exhibit?

• A. A September futures price of $104.00
• B. A September futures price of $96.20
• C. A September futures price of $103.80
• D. A September futures price of $103.61

Best answer: A

What this tests: Element 4 — Derivative Pricing

Explanation: Put-call parity implies that the call-minus-put spread equals the present value of the futures price less the strike when expiry and strike match. Using the exhibit, the option spread is $3.80, and converting that present-value amount to expiry gives a supported futures price of $104.00.

The core idea is put-call parity for European options with the same strike and expiry. With no dividends before expiry, the relationship can be written as \(C-P = DF(F_0-K)\), where \(DF\) is the discount factor and \(F_0\) is the fair forward or futures price under the stated assumption.

So the only supported interpretation is a September futures price of $104.00. Any choice that discounts the spread again, ignores discounting, or reverses the sign misapplies parity.

• The option stating $103.61 multiplies the option spread by the discount factor instead of dividing by it.
• The option stating $103.80 ignores the time-value adjustment and treats the present-value spread as if it were already at expiry.
• The option stating $96.20 reverses the sign of \(C-P\); because the call is worth more than the put, the implied futures price must be above the strike.

With no dividends, \(F_0 = K + (C-P)/DF = 100.00 + (6.00-2.20)/0.95 = \$104.00\).

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Related focused pages

• Free CIRO Derivatives Full-Length Practice Exam
• CIRO Derivatives: Element 1 — the Client Relationship
• CIRO Derivatives: Element 2 — Regulatory Documentation
• CIRO Derivatives: Element 3 — Derivative Types and Features
• CIRO Derivatives: Element 5 — Derivative Trading and Settlement
• CIRO Derivatives: Element 6 — Derivatives Strategies
• CIRO Derivatives: Element 7 — Derivative Market Integrity
• CIRO Derivatives: Element 8 — Conduct and Conflicts

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