Free CISI CMP Sec/Deriv Practice Questions: Derivatives Pricing and Valuation

CISI means Chartered Institute for Securities & Investment. CMP means Capital Markets Programme, and this page is for the Securities/Derivatives unit. Use this focused CISI CMP Securities/Derivatives page as a short practice test for Derivatives Pricing and Valuation. The items are original Finance Prep sample exam questions built for scenario-based practice, not trivia, puzzle questions, official CISI questions, copied live-exam content, or exam dumps.

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These are original Finance Prep practice questions aligned to this topic area. They are not official CISI questions, copied live-exam content, or exam dumps. Use them to preview question style and explanation depth before continuing with topic drills, mixed sets, and timed mock exams in Finance Prep.

Question 1

Topic: Derivatives: Principles of Pricing and Valuation

A derivatives trader is reviewing a three-month equity index futures contract. Assume simple annual rates, proportionate accrual for three months, and no transaction costs, taxes, or margining effect.

Market-data snapshot:

Which is the best supported interpretation?

• A. The fair futures price is about 4,010, so the quoted futures price is rich and a trader could consider selling the futures against buying the underlying basket.
• B. The fair futures price is about 4,050, so the quoted futures price is cheap because expected income should be ignored.
• C. The fair futures price is about 3,990, so the quoted futures price is rich because financing should be subtracted and income added.
• D. The quoted futures price is at fair value because financing cost and expected income offset exactly over the three-month period.

Best answer: A

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: For a simple forward or futures fair value, start with the spot price, add the financing cost of holding the underlying to expiry, and deduct income expected to be received before expiry. Over three months, the financing cost is 5.0% × 3/12 × 4,000 = 50. Expected income is 1.0% × 4,000 = 40. The fair value is therefore 4,000 + 50 - 40 = 4,010. A quoted futures price of 4,040 is above this fair value, so it is rich relative to the cash-and-carry value. In principle, a trader who can finance and hold the underlying could buy the underlying basket and sell the futures, subject to practical costs and execution risks.

• Ignoring expected income overstates fair value because income reduces the cost of carrying the underlying.
• Subtracting financing and adding income reverses the cost-of-carry logic.
• Financing and income do not offset: the three-month financing cost is 50, while expected income is 40.

The fair price is spot plus financing cost less expected income: 4,000 + 50 - 40 = 4,010, making the quoted price of 4,040 above fair value.

Question 2

Topic: Derivatives: Principles of Pricing and Valuation

A trader is checking a junior analyst’s note on the directional effects of valuation inputs. Assume each input is changed in isolation and all other inputs stay constant.

Which interpretation of the option-value drivers is best supported?

• A. Lower spot, lower strike, shorter expiry, higher volatility and lower risk-free rates would support a higher call value; higher expected dividends would increase it.
• B. Higher spot, lower strike, shorter expiry, lower volatility and lower risk-free rates would support a higher call value; higher expected dividends would reduce it.
• C. Higher spot, higher strike, longer expiry, lower volatility and higher expected dividends would support a higher call value; risk-free rates would have little direct effect.
• D. Higher spot, lower strike, longer expiry, higher volatility and higher risk-free rates would support a higher call value; higher expected dividends would reduce it.

Best answer: D

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: A call option becomes more valuable when the underlying price rises because the right to buy at the strike is more likely to be profitable. A lower strike also increases call value because exercise would be at a cheaper price. More time to expiry and higher volatility generally increase option value by giving more opportunity for favourable price moves. Higher risk-free interest rates tend to increase call value because the present value of paying the strike in the future is lower. Expected income from the underlying, such as dividends on an equity index, tends to reduce call value because the option holder does not receive that income before exercise.

• Treating a higher strike or lower volatility as positive for a call reverses the usual directional effects.
• Higher expected dividends are not favourable for a call holder, because dividends reduce the forward value of the underlying.
• Shorter expiry, lower volatility and lower risk-free rates generally reduce, rather than increase, the value of a plain-vanilla call.

For a plain-vanilla equity call, these input changes increase the probability or present value benefit of exercise, while dividends lower the value of holding the option rather than the underlying.

Question 3

Topic: Derivatives: Principles of Pricing and Valuation

A trader is estimating fair values for two 6-month equity index futures contracts. Use simple carry and assume no transaction costs or margin funding effect.

The fair value estimate for Alpha is about 4,070, while the fair value estimate for Beta is about 4,010.

Which pricing input most directly explains the 60-point difference between the two futures values?

• A. Historical volatility of the underlying index
• B. Open interest in the futures contract
• C. Expected dividend points on the underlying index
• D. Initial margin required by the clearing house

Best answer: C

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: For an equity index future, fair value is driven by the spot index level plus financing cost less the value of expected dividends or other income paid before expiry. Here the spot level and financing cost are the same for both contracts. The only pricing input that differs is expected dividend points: Beta has 90 expected dividend points and Alpha has 30. That 60-point dividend difference directly reduces Beta’s fair value relative to Alpha. Volatility is central to option pricing but is not the direct fair-value driver for a straightforward futures carry estimate. Margin and open interest may affect trading, liquidity, or cash management, but they do not explain this arbitrage-free pricing difference under the stated assumptions.

• Initial margin is a collateral requirement, not the carry input causing the stated fair-value gap.
• Historical volatility matters more for option premiums than for this simple futures fair-value estimate.
• Open interest may indicate market participation, but it does not change the carry calculation shown.

Higher expected dividends reduce the fair futures value because futures holders do not receive the cash distributions paid before expiry.

Question 4

Topic: Derivatives: Principles of Pricing and Valuation

A derivatives trader is checking the fair value of a quarterly equity index futures contract before quoting a client.

Pricing facts:

• Current cash index level: 4,200
• Time to futures expiry: 3 months
• Financing rate: 4.8% per annum, simple interest
• Expected dividends on the index over the futures life: 32 index points
• Ignore taxes, bid-offer spread, transaction costs, and margin effects

Using simple cost-of-carry pricing, what is the single best estimate of the fair futures price?

• A. 4,117.6
• B. 4,250.4
• C. 4,218.4
• D. 4,282.4

Best answer: C

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: For a simple forward or futures fair-value calculation, the cost of carry starts with the cash market price, adds the financing cost of holding the underlying to expiry, and subtracts income expected from holding the underlying. Here, the financing cost is 4,200 × 4.8% × 3/12 = 50.4 index points. The expected dividend income is 32 index points. The fair futures price is therefore 4,200 + 50.4 - 32 = 4,218.4. Income reduces the futures price because a holder of the physical index basket receives the dividends, while the futures holder does not receive them directly during the contract life.

• 4,250.4 adds financing but ignores the expected dividend income.
• 4,282.4 adds dividends instead of subtracting them from the cost of carry.
• 4,117.6 incorrectly subtracts both financing and income from the spot index level.

The fair price is spot plus financing for 3 months less dividend income: 4,200 + (4,200 × 4.8% × 3/12) - 32 = 4,218.4.

Question 5

Topic: Derivatives: Principles of Pricing and Valuation

A derivatives trader is checking the price of a three-month equity index futures contract.

Market facts:

• Cash index level: 7,800
• Three-month futures price: 7,760
• Annualised financing rate: 4%
• Expected dividend yield on the index over the period: 6% annualised
• The contract is exchange-traded and cash-settled to the index level at expiry
• Ignore taxes and transaction costs

What is the best explanation for the futures price and expected basis behaviour?

• A. The futures price is lower because initial margin is deducted from the futures value, and the basis should remain unchanged until delivery.
• B. The futures price is below the cash index because expected dividends exceed the financing cost, and the basis should converge towards zero as expiry approaches.
• C. The futures price should be above the cash index because financing cost is positive, so the quoted price indicates an arbitrage-free mispricing.
• D. The futures price is below the cash index because exchange clearing removes counterparty risk, and the discount should widen as expiry approaches.

Best answer: B

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: For an equity index future, the fair price reflects the spot index plus financing cost less the benefit of expected dividends on the underlying shares. Here, the dividend yield of 6% exceeds the financing rate of 4%, giving a negative net cost of carry. That makes a futures price slightly below the cash index consistent with fair pricing. The basis, commonly measured as futures price minus spot price, is therefore negative before expiry. Because the contract is cash-settled to the index level at expiry, the futures price and cash index level should converge as expiry approaches, assuming normal market conditions and no material frictions.

• Clearing reduces counterparty risk but does not by itself create a futures discount or make the basis widen.
• Positive financing cost alone is incomplete because expected dividends must also be included in equity index futures pricing.
• Initial margin is a performance bond, not a deduction from the fair value of the futures contract.

With dividend yield greater than financing cost, fair futures value is below spot, and cash settlement to the index supports convergence at expiry.

Question 6

Topic: Derivatives: Principles of Pricing and Valuation

A derivatives trader buys a listed FTSE 100 index call with these terms:

• Underlying index level at trade: 7,920
• Strike price: 7,800
• Premium paid: 180 index points
• Expiry: three months
• Exercise style: European

Which statement is the single best description of the contract?

• A. The call is at-the-money; its intrinsic value is 180 points and its time value is nil; European style means it can be exercised at any time before expiry.
• B. The call is out-of-the-money; its intrinsic value is nil and its time value is 180 points; the strike price is the premium paid by the buyer.
• C. The call is in-the-money; its intrinsic value is 120 points and its time value is 60 points; European style means it can be exercised only at expiry.
• D. The call is in-the-money; its intrinsic value is 60 points and its time value is 120 points; expiry is the last date on which the premium is paid.

Best answer: C

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: A call option has intrinsic value when the underlying price is above the strike price. Here, the FTSE 100 level of 7,920 is 120 points above the 7,800 strike, so the call is in-the-money with 120 points of intrinsic value. The premium is the total price paid for the option. Any premium above intrinsic value is time value, so the 180-point premium consists of 120 points of intrinsic value and 60 points of time value. The strike price is the exercise price used to determine the payoff, not the premium. Expiry is the date the option ceases to exist. European exercise style means exercise is permitted only at expiry, unlike American style, which allows exercise before expiry.

• Treating the 180-point premium as intrinsic value ignores that only the favourable difference between spot and strike is intrinsic value.
• Calling the position out-of-the-money reverses the call moneyness test, because the index level is above the strike.
• Swapping intrinsic value and time value gives the wrong split of the 180-point premium.
• European style relates to when exercise is permitted, not to the market on which the contract is traded.

For a call, intrinsic value is spot minus strike when positive, so 7,920 - 7,800 = 120, leaving 60 points of time value in the 180-point premium.

Question 7

Topic: Derivatives: Principles of Pricing and Valuation

An equity derivatives desk is reviewing model inputs for a near-the-money, cash-settled European call on a dividend-paying equity index.

Assumptions:

• The call gives upside exposure to the index and has no early exercise feature.
• The pricing review considers each input separately, with other inputs held constant.
• The desk is applying the usual vanilla option pricing relationships for calls.

Which set of input directions would all tend to increase the value of the call?

• A. Lower index level, lower strike, longer time to expiry, higher implied volatility, lower risk-free rate, and higher expected income yield.
• B. Higher index level, lower strike, longer time to expiry, higher implied volatility, higher risk-free rate, and lower expected income yield.
• C. Higher index level, higher strike, longer time to expiry, higher implied volatility, higher risk-free rate, and lower expected income yield.
• D. Higher index level, lower strike, shorter time to expiry, lower implied volatility, lower risk-free rate, and higher expected income yield.

Best answer: B

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: For a vanilla call, value generally rises when the underlying price rises because the right to buy, or receive upside exposure to, the underlying becomes more valuable. A lower strike is also favourable because the exercise price is easier to exceed. Longer time to expiry usually increases time value, and higher implied volatility increases the chance of a favourable payoff while the downside remains limited to the premium. Higher interest rates tend to increase call value because the present value of paying the strike in the future is lower. Expected income from the underlying, such as dividends on an equity index, works against call value because it reduces the expected forward value of the underlying during the option’s life.

• A higher strike makes a call less valuable, even if the other listed inputs are favourable.
• A lower underlying level, lower interest rate, and higher income yield are not favourable to a call.
• Shorter time, lower volatility, and higher expected income all reduce the call’s time or forward-value benefit.

Each listed direction is favourable to a vanilla call’s value when the inputs are considered separately.

Question 8

Topic: Derivatives: Principles of Pricing and Valuation

A commodity futures trader is monitoring the nearby futures contract against the cash market for the same grade and delivery location.

For this contract, basis is defined as cash-market price minus futures price.

Which statement correctly describes the basis at the close and its movement from the opening observation?

• A. The close basis is -£2.30, and the basis has strengthened by £1.20.
• B. The close basis is +£2.30, and the basis has weakened by £1.20.
• C. The close basis is +£1.20, and the basis has weakened by £2.30.
• D. The close basis is -£1.20, and the basis has strengthened by £2.30.

Best answer: D

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: Basis measures the relationship between the cash-market price and the futures price for the same or closely related underlying. Here the stated convention is cash price minus futures price. The opening basis is £212.50 - £216.00 = -£3.50. The close basis is £214.00 - £215.20 = -£1.20. A move from -£3.50 to -£1.20 is an increase of £2.30, so the basis has strengthened or narrowed. The cash price is still below the futures price, but by a smaller amount than before.

• A positive close basis reverses the stated calculation; the cash price is below the futures price at the close.
• A close basis of -£2.30 confuses the basis movement with the actual close basis.
• A weakening basis would move lower, not from -£3.50 up to -£1.20.

The close basis is £214.00 - £215.20 = -£1.20, compared with an opening basis of -£3.50, so it has strengthened by £2.30.

Question 9

Topic: Derivatives: Principles of Pricing and Valuation

A derivatives trader is checking whether quoted European options are consistent with put-call parity. Ignore transaction costs, bid-offer spread, stock borrow constraints, and counterparty credit risk.

Market-data snapshot:

Which interpretation or action is best supported by the snapshot?

• A. The protective put is overpriced relative to the fiduciary call; buy the call and lend £98, while selling the share and put.
• B. The call is underpriced relative to the put; buy the call and sell the put without taking an underlying or financing position.
• C. The fiduciary call is overpriced relative to the protective put; buy the share and put, sell the call, and borrow £98.
• D. Parity is satisfied because the call premium exceeds the put premium and the spot price exceeds the present value of the strike.

Best answer: C

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: Put-call parity links European calls and puts with the same strike and expiry on a non-dividend-paying underlying: long call plus the present value of the strike is economically equivalent to long put plus the underlying. Both combinations deliver the same expiry payoff. Here, the fiduciary call costs £7 + £98 = £105. The protective put costs £100 + £4 = £104. Since the payoff is the same but prices differ, the higher-priced combination should be sold and the lower-priced combination bought. Selling the call and borrowing £98 is the short fiduciary-call side; buying the share and put is the lower-priced protective put side.

• Treating parity as satisfied overlooks that call plus present value of strike is £105, while put plus share is £104.
• Buying the call and lending cash while selling the share and put is the reverse trade; it buys the dear side and sells the cheap side.
• Buying the call and selling the put alone leaves a synthetic forward exposure and does not lock in the parity difference against the share and financing leg.

Put-call parity requires the call plus present value of the strike to equal the put plus share, and the snapshot shows £105 versus £104.

Question 10

Topic: Derivatives: Principles of Pricing and Valuation

An equity derivatives trader is making a quick estimate for a European call on a dividend-paying share. The current call premium is £5.20. Around the current level, the desk uses these one-factor estimates:

A proposed comparable call has:

• underlying share price £2 higher;
• strike price £1 higher;
• one month less to expiry;
• implied volatility 3 percentage points higher;
• risk-free interest rate 1 percentage point higher;
• expected dividend yield 2 percentage points higher.

Using the desk’s estimates, what is the approximate premium for the proposed call?

• A. £5.72
• B. £5.90
• C. £6.80
• D. £6.06

Best answer: B

What this tests: Derivatives: Principles of Pricing and Valuation

Explanation: Start with the current premium of £5.20. For a call, a higher underlying price, higher volatility, and higher interest rates increase value. A higher strike, shorter time to expiry, and higher expected dividends reduce value. The effects are: share price +£1.10, strike -£0.45, shorter expiry -£0.08, volatility +£0.18, interest rate +£0.03, and dividends -£0.08. The net movement is +£0.70, so the estimated premium is £5.90. This is a local estimate using the supplied sensitivities, not a full repricing model.

• £5.72 ignores the volatility increase; higher expected volatility raises option time value.
• £6.06 gives a favourable sign to either shorter expiry or higher income, but both reduce the call premium under the stated estimates.
• £6.80 treats a higher strike as favourable, but a higher strike makes a call less valuable.

The stated effects add a net £0.70 to the current £5.20 premium, giving an estimated call premium of £5.90.

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