You’re on a roll
Create a free account to save your FRM progress, track your accuracy by topic, and pick up right where you left off.
Free Questions › FRM › Financial Markets and Products
Free FRM Financial Markets and Products Practice Questions & Answers
400 exam-style Financial Markets and Products questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 271
The 'Greeks sensitivity' chain for a barrier option differs from vanilla options because:
Select an option first.
Correct answer: B — Delta and gamma can be very large near the barrier — as the underlying approaches the knock-in or knock-out level, small price moves can dramatically change whether the option exists, causing delta to spike
Explanation: B is correct: near the barrier level, the existence of the option is highly sensitive to small price movements. For a knock-out option approaching its barrier, the option value can collapse discontinuously as the barrier is crossed, leading to very large (negative) delta and gamma instability. This makes dynamic hedging of barrier options challenging near the barrier. A is wrong — barrier options do have Greeks. C is wrong — not delta-neutral. D is wrong — gamma can be extremely large and either positive or negative near the barrier.
Question 272
In the context of weather derivatives, 'heating degree days' (HDD) are calculated as:
Select an option first.
Correct answer: B — max(0, 65°F − daily average temperature) — accumulating when temperatures are cold, indicating heating demand
Explanation: B is correct: HDD for a given day = max(0, 65°F − daily average temp). For example, if the average temperature is 50°F, HDD = 15. These accumulate over a season to give a seasonal HDD index. Energy companies use HDD derivatives to hedge exposure to warm winters (lower heating demand → lower revenue). A is wrong — that would be CDD (cooling). C and D are wrong — HDD uses 65°F as base.
Question 273
A 'cross-hedge' uses a futures contract on a different underlying from the hedged position. The key risk in a cross-hedge is:
Select an option first.
Correct answer: B — Basis risk — the correlation between the futures contract's underlying and the hedged position may be imperfect, causing the hedge to be less effective
Explanation: B is correct: a cross-hedge (e.g. hedging jet fuel risk with crude oil futures) introduces basis risk — the correlation between jet fuel prices and crude oil futures is high but not perfect. Any divergence between the two creates hedging error. The hedge ratio is calibrated using regression (h* = ρ × σ_S/σ_F) to minimise this basis risk. A is wrong — futures on specific assets do not exist for all underlyings. C is wrong — exchange-traded futures have minimal counterparty risk. D is wrong — cross-hedges are used in commodities, equities, and interest rates.
Question 274
Eurodollar futures are used to construct an 'implied forward rate curve'. From successive Eurodollar contract prices (100 − rate), the implied forward 3-month rates can be read as:
Select an option first.
Correct answer: B — The market's expectation of the 3-month USD rate at each future contract date — by chaining these together, a forward rate curve extending 10+ years can be constructed
Explanation: B is correct: each Eurodollar futures contract implies a 3-month forward rate starting at the contract's expiry date. For example, the June contract implies the 3-month rate starting in June. By linking together quarterly Eurodollar contracts (or SOFR futures), a detailed forward rate curve can be constructed extending many years, used for swap pricing and risk management. A is wrong — spot rate comes from the nearest contract. C is wrong — Eurodollar is short-term. D is wrong — implied forwards are market-derived, not Fed projections.
Question 275
The 'swap tenor' refers to:
Select an option first.
Correct answer: B — The total duration of the swap contract from inception to final payment date
Explanation: B is correct: tenor is the total time from the start (effective date) to the end (termination date) of the swap. A 5-year USD fixed-for-floating SOFR swap has a tenor of 5 years with semi-annual fixed payments and quarterly floating payments. A is wrong — credit quality is the counterparty's creditworthiness. C is wrong — reset frequency is specified separately. D is wrong — notional is the reference amount for payment calculation.
Get the full FRM question bank — free
Drop your email and we'll send you fresh FRM practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Want to save your score and take a full mock exam? Create a free account →
Question 276
When futures markets are in 'contango', rolling a long commodity futures position from one contract to the next (further dated):
Select an option first.
Correct answer: B — Incurs a negative roll yield — more expensive further-dated contracts are purchased as cheaper near-term contracts mature/expire
Explanation: B is correct: in contango (F > S), the near-term futures are cheaper than the far-dated ones. When a long futures position is rolled forward (sell the expiring contract, buy the next one), you sell low (near-term) and buy high (far-dated), incurring a cost — negative roll yield. This is a persistent drag for long-only commodity index strategies in contango markets. A is wrong — positive roll yield occurs in backwardation. C is wrong — roll yield significantly affects returns. D is wrong — rolling in contango is costly.
Question 277
A 'structured note' is a fixed income security with a return linked to an underlying market variable. A common example is:
Select an option first.
Correct answer: B — A principal-protected note where the return is linked to an equity index return — investors receive their principal back plus participation in upside equity returns
Explanation: B is correct: structured notes embed derivatives (options, swaps) into a note format, allowing investors to gain customised exposures. Examples include: equity-linked notes (principal + call option on index); range accrual notes; and CMS-linked notes. These are used to meet specific investor return requirements while managing risk exposure. A is wrong — plain government bonds are not structured. C is wrong — money market instruments are not structured. D is wrong — inflation-linked bonds are a separate asset class.
Question 278
In a 'carry trade' with interest rate futures, an investor benefits from:
Select an option first.
Correct answer: B — Earning positive carry by holding higher-yielding positions funded at lower rates — rolling futures contracts in a normal (upward-sloping) yield curve generates roll-down return
Explanation: B is correct: in an upward-sloping yield curve environment, rolling a long futures position from the near-term to the next contract generates roll-down return — as time passes, a bond 'slides down' the yield curve (its maturity shortens, typically moving to a lower yield point), causing its price to increase. For futures, this manifests as positive carry from the term structure. A is wrong — high volatility is unfavorable for carry. C is wrong — rising rates hurt long bond positions. D is wrong — falling futures prices would be a loss.
Question 279
The 'repo rate' on a general collateral (GC) repo versus a 'special' repo differs in that:
Select an option first.
Correct answer: B — Special repos have lower rates than GC repos because the collateral (specific bond) is in high demand for short-selling — lenders accept lower rates to obtain the specific bond
Explanation: B is correct: a 'special' repo involves a specific bond that is in high demand (e.g. a recently-issued on-the-run Treasury that many investors want to borrow for short-selling). To borrow this specific bond, the lender accepts a lower interest rate (the 'specialness' means the borrower extracts additional value). GC repos use any qualifying collateral and price at the general market rate. A is wrong — special repo rates are lower, not higher. C is wrong — special repos settle normally. D is wrong — both can be electronic.
Question 280
In pricing a forward on a dividend-paying stock using the cost-of-carry model, the known dividends during the forward period:
Select an option first.
Correct answer: B — Are subtracted from the current stock price (as present value) before computing the forward price: F = (S₀ − PV(D)) × e^{rT}
Explanation: B is correct: dividends received by the stock holder during the holding period represent an income that reduces the effective cost of carry. The forward price is: F = (S₀ − PV(dividends)) × e^{rT}. The present value of dividends is deducted from the current spot price because the stock holder (not the forward holder) receives the dividends. A is wrong — dividends reduce (not increase) the forward price. C is wrong — dividends clearly affect the forward price. D is wrong — dividends are discounted, not multiplied by r.
Question 281
The 'swap spread' compressed significantly in the US post-2008. This was primarily due to:
Select an option first.
Correct answer: B — Regulatory changes requiring banks to post collateral on swaps (OIS discounting) and the introduction of CCP clearing — reducing the credit component of swap spreads
Explanation: B is correct: multiple factors compressed US swap spreads post-2008: (1) mandatory CCP clearing reduced counterparty risk; (2) transition to OIS discounting reduced the credit component; (3) abundant Treasury supply (QE unwinding) pushed Treasury yields up. These structural changes reduced the credit risk premium embedded in swap rates vs Treasuries, compressing or even inverting the swap spread. A is wrong — bank credit risk was high post-crisis but swaps became less risky. C is wrong — Treasury issuance increased substantially. D is wrong — central banks do not buy swaps.
Question 282
In futures markets, the 'settlement price' is used for:
Select an option first.
Correct answer: B — Calculating daily variation margin — it is typically set near the closing price and used to mark all open positions to market at the end of each trading day
Explanation: B is correct: the daily settlement price (closing price) is determined by the exchange (often using a volume-weighted average near the close) and is used to calculate each participant's daily profit or loss, which is then settled through variation margin. A is wrong — the last traded price may differ from the settlement price. C is wrong — initial margin is set by the exchange/CCP based on volatility, not the settlement price. D is wrong — conversion factors are predetermined.
Question 283
A 'window forward' in FX markets is:
Select an option first.
Correct answer: B — A forward contract that allows the buyer to take delivery at any time within a specified window (date range) — providing flexibility while still providing exchange rate certainty
Explanation: B is correct: a window forward (or time option forward) gives the corporate hedger the right to deliver/receive currency at any point within a specified date range (the window) at the agreed forward rate. This provides flexibility for companies with uncertain timing of foreign currency cash flows while locking in the exchange rate. A is wrong — that is a standard forward. C is wrong — the exchange rate is fixed. D is wrong — window forwards are not options; they are binding contracts with timing flexibility.
Question 284
Under interest rate parity (IRP), the covered IRP condition states that:
Select an option first.
Correct answer: B — The forward exchange rate premium/discount exactly offsets the interest rate differential between two countries — preventing riskless arbitrage through borrowing in one currency and investing in another
Explanation: B is correct: covered IRP (CIP): F/S = (1 + r_d)/(1 + r_f), where F is the forward rate, S is the spot rate, r_d is the domestic rate and r_f is the foreign rate. If this relationship is violated, riskless arbitrage is possible (borrow domestically, invest abroad, sell the foreign currency forward). CIP is generally well-enforced in liquid FX markets. A is wrong — that involves real rates (purchasing power parity). C is wrong — uncovered IRP is a weaker condition (without hedging). D is wrong — forward rates are market-determined.
Question 285
The 'strike price' of an interest rate cap determines:
Select an option first.
Correct answer: B — The maximum floating interest rate the cap buyer will effectively pay — above the strike, the cap pays the excess rate × notional × period
Explanation: B is correct: the cap strike (or cap rate) K is the interest rate above which the cap provides protection. Each caplet pays max(0, L − K) × notional × Δt at the end of each period, where L is the reference rate. The cap buyer (typically a floating-rate borrower) effectively caps their borrowing cost at K plus the credit spread. A is wrong — the strike relates to the reference rate, not the coupon. C is wrong — notional is separately specified. D is wrong — settlement frequency is a separate term.
Question 286
'Volatility of volatility' (vol of vol) is a key concept in:
Select an option first.
Correct answer: B — Stochastic volatility models (e.g. Heston model) where the volatility itself is a random process — vol of vol determines the curvature of the implied volatility smile
Explanation: B is correct: in stochastic volatility models like Heston, the asset price and its volatility are both stochastic. The 'vol of vol' parameter (ξ in Heston) determines how much the volatility itself fluctuates — higher vol of vol creates a more pronounced volatility smile/skew. This parameter is critical for pricing exotic options sensitive to the curvature of the volatility surface. A is wrong — simple delta hedging uses constant vol (BSM). C is wrong — vol of vol is a derivatives concept. D is wrong — commodity forward pricing uses cost-of-carry.
Question 287
A 'participating forward' is an FX product that:
Select an option first.
Correct answer: B — Gives the buyer downside protection (via a put) while allowing partial participation in favourable rate moves — typically structured at zero net premium by combining a forward with an option
Explanation: B is correct: a participating forward combines a full forward hedge with a partial option on the upside. For example, a company hedging USD sales might buy a participating forward that guarantees a minimum USD/EUR rate but allows them to benefit from 50% of any USD strengthening beyond the strike. The structure is zero-cost (net premium = 0). A is wrong — a standard forward has no upside. C is wrong — a participating forward has optionality. D is wrong — that is a standard forward.
Question 288
A call option gives the holder the right to:
Select an option first.
Correct answer: B — Buy the underlying asset at the strike price on or before the expiry date
Explanation: B is correct: a call option gives the buyer (holder) the right, but not the obligation, to purchase the underlying asset at the predetermined strike price on or before (American) or on (European) the expiration date. A is wrong — selling right is a put option. C is wrong — fixed interest is a bond feature. D is wrong — the option buyer has the right to buy, not the seller.
Question 289
A put option gives the holder the right to:
Select an option first.
Correct answer: B — Sell the underlying asset at the strike price on or before the expiry date
Explanation: B is correct: a put option gives the holder the right (not obligation) to sell the underlying asset at the strike price. The holder exercises the put if the market price falls below the strike, generating a profit equal to (K − S) per unit. A is wrong — that is a call option. C is wrong — that describes the payoff, not the right. D is wrong — the put holder forces the counterparty to buy, not sell.
Question 290
The intrinsic value of a call option with strike K and underlying price S is:
Select an option first.
Correct answer: B — max(0, S − K) — the immediate exercise value, zero if out-of-the-money
Explanation: B is correct: intrinsic value of a call = max(0, S − K). If S > K, the option is in-the-money and has positive intrinsic value. If S ≤ K, the option is at or out-of-the-money with zero intrinsic value. A is wrong — K − S is put intrinsic value. C is wrong — option premium includes time value. D is wrong — not additive.
Question 291
The time value of an option is:
Select an option first.
Correct answer: B — Option premium minus intrinsic value — represents the value of the right to wait, which depends on volatility, time to expiry, and interest rates
Explanation: B is correct: time value = option price − intrinsic value. It captures the possibility that the option may move further into the money before expiry. Time value declines to zero at expiry (theta decay). A is wrong — intrinsic value is separate. C is wrong — European options have time value. D is wrong — not a formula for time value.
Question 292
For a European call option, which of the six factors increases its value?
Select an option first.
Correct answer: C — Higher underlying asset price
Explanation: C is correct: the six factors affecting option price are: (1) underlying asset price (positive for call, negative for put); (2) strike price (negative for call, positive for put); (3) time to expiry (positive for both); (4) volatility (positive for both); (5) risk-free rate (positive for call, negative for put); (6) dividends (negative for call, positive for put). A higher underlying price increases call value. A is wrong — higher strike reduces call value. B is wrong — less time to expiry reduces call value. D is wrong — higher risk-free rate helps calls, not puts.
Question 293
Higher volatility of the underlying asset increases the value of both call and put options because:
Select an option first.
Correct answer: B — Option holders benefit from increased upside potential while their downside is limited to the premium paid — higher volatility increases the probability of large movements in either direction
Explanation: B is correct: the asymmetric payoff of options means that holders benefit from larger price swings in the favourable direction while losing only the premium for unfavourable movements. Higher volatility increases the probability of the option expiring deep in-the-money, increasing its expected value for both calls and puts. A is wrong — volatility affects the distribution, not just the mean. C is wrong — volatility increases the probability of exercise. D is wrong — volatility benefits all options, including out-of-the-money.
Question 294
Put-call parity for European options on a non-dividend-paying stock states:
Select an option first.
Correct answer: B — C − P = S − K × e^(−rT) or equivalently C + PV(K) = P + S
Explanation: B is correct: put-call parity states C + K × e^{−rT} = P + S₀, which rearranges to C − P = S₀ − K × e^{−rT}. This is the no-arbitrage relationship between European call and put prices with the same strike and expiry on the same non-dividend-paying underlying. A presents the same equation correctly but in a slightly different form — both A and B are equivalent. B presents it in the standard textbook form. A is also correct but B is the more standard form.
Question 295
A covered call strategy involves:
Select an option first.
Correct answer: B — Holding the underlying asset and selling (writing) a call option — generates premium income but caps upside above the strike price
Explanation: B is correct: a covered call is long the stock + short a call. The call premium provides income (protecting slightly against price declines) but caps the upside at the strike price. If the stock rises above the strike, the call is exercised and the stock is called away at the strike. A is wrong — that is not a covered call. C is wrong — that is a straddle. D is wrong — selling the underlying creates a synthetic short covered call (different strategy).
Question 296
A protective put involves:
Select an option first.
Correct answer: B — Holding the underlying asset and buying a put option — provides downside protection while maintaining upside potential
Explanation: B is correct: a protective put = long stock + long put. The put acts like insurance — if the stock falls below the strike, the put can be exercised to sell at the strike price, limiting downside. The upside is unlimited. B is correct. A is wrong — cash + put is a different strategy. C is wrong — that is a risk reversal. D is wrong — writing a put is selling downside protection, not buying it.
Question 297
The Black-Scholes-Merton (BSM) model assumes:
Select an option first.
Correct answer: A — Stock returns are normally distributed and the stock price follows a geometric Brownian motion with constant volatility
Explanation: A is correct: the BSM model assumes: (1) stock price follows geometric Brownian motion (lognormal prices, normally distributed returns); (2) constant risk-free rate and volatility; (3) no dividends in the basic model; (4) continuous trading; (5) no transaction costs; (6) European options. A correctly describes the key assumption. B is wrong — BSM assumes no jumps (jump-diffusion models extend BSM). C is wrong — dividends can be incorporated (continuous dividend yield). D is wrong — BSM assumes a constant risk-free rate.
Question 298
The BSM formula for a European call option on a non-dividend-paying stock is:
Select an option first.
Correct answer: A — C = S × N(d₁) − K × e^(−rT) × N(d₂)
Explanation: A is correct: the BSM call price formula is C = S₀ × N(d₁) − K × e^{−rT} × N(d₂), where d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d₂ = d₁ − σ√T. N(·) is the standard normal CDF. B is wrong — the subtraction is reversed. C is wrong — d₁ and d₂ are swapped. D is wrong — not the correct formula.
Question 299
Delta (Δ) of a European call option is:
Select an option first.
Correct answer: B — N(d₁) — the rate of change of the call price with respect to the underlying asset price, ranging from 0 (deep OTM) to 1 (deep ITM)
Explanation: B is correct: delta measures the sensitivity of the option price to a $1 change in the underlying asset price. For a European call, Δ = N(d₁), which ranges from 0 (far OTM, unlikely to expire ITM) to 1 (far ITM, near-certainty of exercise). A is wrong — delta is only 1 for deep ITM calls. C is wrong — that describes vega. D is wrong — the hedge ratio is 1/delta, not delta.
Question 300
Gamma (Γ) of an option measures:
Select an option first.
Correct answer: B — The rate of change of delta with respect to the underlying asset price — the curvature of the option price-underlying relationship
Explanation: B is correct: gamma is the second derivative of option price with respect to underlying price, or equivalently, the rate of change of delta. High gamma means delta changes rapidly with small moves in the underlying. Gamma is highest for at-the-money options near expiry. A is wrong — that is vega. C is wrong — that is theta. D is wrong — that is rho.
More free FRM topics
Ten questions in
- The ones you miss are saved as a drill you can repeat
- Your place is kept, on this device and any other
- A streak, if that is the thing that gets you back tomorrow
Every question on this page stays free and open either way.