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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 331
Credit default swaps (CDS) are instruments where:
Select an option first.
Correct answer: B — The protection buyer pays periodic premiums (CDS spread) to the protection seller, who agrees to compensate the buyer if a specified credit event (default, restructuring) occurs on the reference entity
Explanation: B is correct: a CDS is essentially credit insurance. The protection buyer pays a periodic spread (the CDS spread, expressed in bps per annum × notional) to the protection seller. If a defined credit event occurs, the seller pays the buyer the loss (face value − recovery value). A is wrong — CDS is not an exchange of fixed coupons. C is wrong — CDS can be physically or cash settled. D is wrong — the CDS spread ≈ credit spread above the risk-free rate, not the full YTM.
Question 332
When the term structure of volatility shows that implied volatility is higher for shorter-dated options (volatility term structure inverted), this typically suggests:
Select an option first.
Correct answer: B — The market expects near-term uncertainty to be elevated (perhaps due to an impending event) relative to long-term conditions
Explanation: B is correct: an inverted volatility term structure (short-dated IV > long-dated IV) typically indicates that the market anticipates higher near-term uncertainty — perhaps due to an upcoming earnings announcement, election, central bank decision, or geopolitical event. Over the longer term, volatility is expected to revert to a lower level. A is wrong — that describes a normal (upward-sloping) term structure. C is wrong — an inverted term structure actually violates BSM's constant volatility assumption. D is wrong — option price depends on many factors.
Question 333
A principal-protected note (PPN) is typically constructed as:
Select an option first.
Correct answer: B — A zero-coupon bond (to return principal at maturity) plus a long position in a call option (to provide upside participation in the underlying)
Explanation: B is correct: a PPN guarantees return of principal at maturity while offering participation in the upside of a reference asset. It is structured as: zero-coupon bond (priced at a discount = PV of face value at maturity) + long call option (providing upside). If the reference asset rises, the call pays off; if it falls, the ZCB alone returns the principal. A is wrong — a short call limits upside; the PPN wants upside. C is wrong — inverse floaters have different structures. D is wrong — PPN includes an option, not just bonds.
Question 334
American option pricing using the binomial model:
Select an option first.
Correct answer: B — Tests at each node whether immediate exercise value exceeds the continuation (hold) value — the option value at each node is the maximum of intrinsic value and the present value of expected future values
Explanation: B is correct: the key feature of American option pricing in the binomial model is that at each node, the option value = max(exercise value, PV of expected future values). This correctly models the early exercise feature by checking at every node whether it is optimal to exercise immediately. A is wrong — the binomial model handles American options explicitly. C is wrong — BSM is only for European options. D is wrong — early exercise is tested and permitted.
Question 335
In the context of mortgage-backed securities, the 'pass-through' structure means:
Select an option first.
Correct answer: B — All principal and interest payments from the mortgage pool (minus servicing fees) are passed through directly to investors on a pro-rata basis
Explanation: B is correct: in a pass-through MBS, the servicer collects mortgage payments from borrowers and passes them through (minus fees) to investors proportionally. All investors in the same class receive the same pro-rata share of cash flows — there is no tranching in a basic pass-through. A is wrong — distributions occur monthly. C is wrong — both principal and interest pass through. D is wrong — fees are deducted, but cash flows pass through promptly.
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Question 336
The relationship between an option's delta and the risk-neutral probability of the option expiring in-the-money is:
Select an option first.
Correct answer: B — In the BSM model, N(d₂) is the risk-neutral probability of a European call expiring in-the-money, while N(d₁) is the option's delta — the two differ due to the convexity of the payoff
Explanation: B is correct: in BSM, N(d₂) is the risk-neutral probability that S_T > K (option expires ITM), while N(d₁) = delta (the hedge ratio). They differ because the payoff at exercise equals S_T (not a fixed amount), creating a difference between the probability and the delta. N(d₁) > N(d₂) since d₁ > d₂ (d₁ = d₂ + σ√T). A is wrong — they differ. C is wrong — they differ by σ√T. D is wrong — only N(d₂) is the risk-neutral probability.
Question 337
An 'Asian option' (average rate option) differs from a vanilla option because:
Select an option first.
Correct answer: B — Its payoff depends on the average price of the underlying over the option's life rather than just the terminal price — this reduces the option's value since averaging dampens extreme outcomes
Explanation: B is correct: an Asian option's payoff is based on the average price of the underlying over a specified period (e.g. the average of daily closing prices). The average is less volatile than the terminal spot price, so Asian options are cheaper than equivalent vanilla options. They are widely used in commodity risk management. A is wrong — that describes a European option. C is wrong — Asian options are traded globally. D is wrong — they typically have a strike price.
Question 338
A 'barrier option' is triggered when:
Select an option first.
Correct answer: B — The underlying asset price reaches a specified barrier level — either activating (knock-in) or extinguishing (knock-out) the option
Explanation: B is correct: barrier options have payoffs contingent on whether the underlying touches a specified price level. A knock-in option becomes active (comes into existence) only if the barrier is hit. A knock-out option is terminated (worthless) if the barrier is hit. These are cheaper than vanilla options because there is a chance the option will not exist or will be extinguished. A is wrong — moneyness at expiry is the vanilla option condition. C is wrong — volatility triggers are different instruments. D is wrong — time triggers are different.
Question 339
The price of a 'lookback option' at expiry depends on:
Select an option first.
Correct answer: B — The minimum (or maximum) price of the underlying over the option's life — a lookback call pays max(S_T − S_min, 0), allowing the holder to buy at the lowest historical price
Explanation: B is correct: a floating-strike lookback call pays max(S_T − S_min, 0) where S_min is the minimum stock price achieved during the option's life. This gives the holder the right to buy at the historical minimum — eliminating the regret of not buying at the lowest point. A is wrong — terminal price alone is the vanilla option case. C is wrong — average determines Asian option. D is wrong — variance determines variance swaps.
Question 340
A 'chooser option' gives the holder the right to decide:
Select an option first.
Correct answer: B — Whether the option is a call or a put — the decision is made at a specified interim date, with exercise at the final expiry
Explanation: B is correct: a chooser option allows the holder to choose, at a specified decision date, whether the instrument will be a call or a put (both with the same strike and final expiry). It is useful when the direction of price movement is uncertain. A is wrong — early exercise is an American feature. C is wrong — the underlying is specified at inception. D is wrong — settlement method is not the choice.
Question 341
The yield to maturity (YTM) and the internal rate of return (IRR) of a bond are related because:
Select an option first.
Correct answer: B — The YTM is the IRR of the bond's cash flows — the discount rate that equates the present value of all future cash flows (coupons + principal) to the bond's current market price
Explanation: B is correct: YTM is exactly the IRR of the bond's cash flows when the bond is priced at market. YTM = IRR iff the bond is held to maturity, and all coupon payments are reinvested at the YTM rate. B correctly identifies the relationship. A is wrong — they are equal only when the bond is priced at market (which is the definition of YTM). C is wrong — both use nominal cash flows. D is wrong — they are equal for plain fixed-rate bonds.
Question 342
A floating rate note (FRN) is valued close to par at each coupon reset date because:
Select an option first.
Correct answer: A — The coupon is set equal to the discount rate at each reset, so the present value of future coupons and principal equals par
Explanation: A is correct: at each coupon reset date, the next coupon is set equal to the current benchmark rate (e.g. SOFR). Discounting this coupon at the same rate gives a PV of par for the remaining cash flows (since coupon rate = discount rate → bond prices at par). Between reset dates, FRNs may deviate from par due to spread changes or credit quality changes. B is wrong — there is no government guarantee for most FRNs. C is wrong — FRN duration is short (≈ next reset date). D is wrong — credit spreads cause deviations.
Question 343
The 'clean price' of a bond is used in market quotations because:
Select an option first.
Correct answer: B — It removes the accrued interest component, making the quoted price reflect only the pure time value and credit risk changes — not the mechanical accumulation of interest between coupon dates
Explanation: B is correct: if bonds were quoted at dirty price (full price), the quoted price would increase monotonically between coupon dates (just due to accrued interest), even if yield conditions were unchanged. Using clean price removes this 'noise', so changes in the quoted price purely reflect changes in yield or credit quality. A is wrong — clean price still includes all future cash flows in its underlying PV. C is wrong — clean price requires subtracting accrued interest (more steps). D is wrong — different markets use different conventions.
Question 344
An interest rate caplet is a call option on the reference rate. Using Black's model, its value depends on:
Select an option first.
Correct answer: B — The current forward rate for the relevant period, the cap strike rate, time to caplet expiry, and the implied volatility of forward rates (cap volatility)
Explanation: B is correct: Black's model for a caplet uses: F (forward rate for the reference period), K (cap strike), T (time to caplet expiry), σ (cap volatility/normal or lognormal implied volatility), and r (discount rate). This is analogous to BSM but applied to interest rate levels. A is wrong — that is BSM for equity options. C is wrong — the forward rate and volatility are both needed. D is wrong — swaption volatility is for swaptions, not caplets.
Question 345
The duration of a zero-coupon bond equals:
Select an option first.
Correct answer: B — Exactly its maturity in years — since the only cash flow is at maturity, there is no averaging effect from interim coupon payments
Explanation: B is correct: for a zero-coupon bond, all cash flows occur at a single date (maturity). The Macaulay duration is therefore exactly equal to the time to maturity. This makes zero-coupon bonds useful for precise duration targeting in immunisation strategies. A is wrong — zero-coupon bonds have no coupons (that's the defining feature). C is wrong — the duration-yield relationship is more complex. D is wrong — duration = maturity for zero coupons.
Question 346
A callable bond has negative convexity in which region?
Select an option first.
Correct answer: B — When the bond is close to or at the call boundary (rates near or below the coupon rate) — the call option limits price appreciation
Explanation: B is correct: negative convexity for callable bonds occurs when rates fall enough that the call option becomes likely to be exercised. The price appreciation is capped because the issuer will likely call the bond at the call price, preventing the bond from rising above the call price. When rates are well above the call threshold, the callable bond behaves like a straight bond with positive convexity. A is wrong — deep OTM call → bond behaves like a straight bond. C is wrong — only near the call boundary. D is wrong — too specific.
Question 347
The 'constant maturity swap' (CMS) rate refers to:
Select an option first.
Correct answer: B — A reference rate equal to the swap rate for a specified maturity (e.g. 10-year swap rate) that is observed periodically and used as a floating rate in a CMS swap
Explanation: B is correct: in a CMS product, the floating rate is not a short-term rate (like SOFR) but rather the par swap rate for a fixed tenor (e.g. the 10-year USD swap rate) observed on each reset date. CMS swaps and CMS caps/floors are used to gain exposure to the slope of the yield curve. A is wrong — 'constant maturity' refers to a fixed tenor of the reference rate, not a non-changing maturity. C is wrong — perpetual swaps are different. D is wrong — that describes an OIS.
Question 348
The Greeks 'charm' measures:
Select an option first.
Correct answer: B — The rate of change of delta with respect to the passage of time (also called delta decay) — important for delta-hedging as options approach expiry
Explanation: B is correct: charm = ∂Δ/∂t. It measures how the delta of an option changes as time passes. For a near-the-money option approaching expiry, charm can be significant — the delta of a call approaches 0 (OTM) or 1 (ITM) rapidly near expiry. Delta-hedgers need to account for charm when they cannot rebalance continuously. A is wrong — that is vanna. C is wrong — that is speed. D is wrong — second-order yield sensitivity is related to convexity.
Question 349
In mortgage finance, the 'weighted average coupon' (WAC) of an MBS pool represents:
Select an option first.
Correct answer: B — The average coupon rate of the underlying mortgages, weighted by their outstanding balances — represents the gross interest income available to pay MBS investors
Explanation: B is correct: WAC = Σ(balance_i × coupon_i) / Σ(balance_i). It represents the weighted average of all mortgage interest rates in the pool. The net coupon to MBS investors is WAC minus servicing/guarantee fees. WAC changes over time as mortgages with different rates prepay. A is wrong — YTM requires market pricing. C is wrong — WAC minus fees gives the pass-through rate. D is wrong — CPR is a prepayment measure.
Question 350
In a CMO (collateralised mortgage obligation), the PAC (planned amortisation class) tranche is designed to:
Select an option first.
Correct answer: B — Provide highly predictable cash flows by absorbing prepayment and extension risk within a defined PSA collar — prepayment risk is passed to support (companion) tranches outside the collar
Explanation: B is correct: PAC bonds are designed to have stable, predictable cash flows within a specified prepayment band (PSA collar). Companion tranches absorb the prepayment volatility when prepayment speeds are above or below the PAC band. When prepayment is within the collar, PAC investors receive the scheduled principal. B is correct. A is wrong — companions absorb risk, not PAC. C is wrong — sequential pay tranches receive principal first. D is wrong — PAC bonds receive both principal and interest.
Question 351
The 'interest-only' (IO) tranche in a CMO receives:
Select an option first.
Correct answer: B — Only the interest portion of mortgage payments — its value increases when prepayments slow (more interest payments continue longer) and decreases dramatically when prepayments accelerate
Explanation: B is correct: IO tranches receive the interest cash flows from the pool. Their value is inversely related to prepayment speeds: slow prepayment → more outstanding principal → more interest → IO is more valuable. Fast prepayment → principal paid down quickly → less interest → IO value falls sharply. IO strips have negative duration (unusual for fixed income). B is correct. A is wrong — that describes a PO (principal-only) tranche. C is wrong — IO and PO are separated. D is wrong — IO cash flows depend on prepayments.
Question 352
The 'principal-only' (PO) tranche in a CMO benefits from:
Select an option first.
Correct answer: B — Fast prepayment speeds — receiving the principal face value sooner (at a discount) results in higher yield; PO bonds are purchased at a discount to face value
Explanation: B is correct: PO strips are purchased at a significant discount to face value. The holder receives the face value whenever principal is paid. Fast prepayment means the full face value is received sooner, improving the internal rate of return. PO strips have positive duration and benefit from falling rates (which increase prepayments). A is wrong — slow prepayment delays cash flows, reducing PO value. C is wrong — rising rates reduce prepayments, hurting PO. D is wrong — PO cash flows are highly dependent on prepayment.
Question 353
Which of the following is an 'exotic' option rather than a 'vanilla' option?
Select an option first.
Correct answer: B — A path-dependent barrier option that activates only if the S&P 500 crosses a specified level during the option's life
Explanation: B is correct: exotic options have non-standard features beyond simple calls and puts. Barrier options, Asian options, lookback options, chooser options, compound options, and digital options are all exotic. B describes a knock-in barrier option — an exotic. A, C and D are all vanilla (standard) options. B is correct.
Question 354
In the Vasicek and CIR models, 'mean reversion' in interest rates means:
Select an option first.
Correct answer: B — Rates tend to be pulled back toward a long-run average level — if rates are above the long-run mean, they tend to fall; if below, they tend to rise
Explanation: B is correct: mean reversion is the property that interest rates (and many other financial variables) tend to return to a long-run equilibrium level. In Vasicek: dr = a(b − r)dt + σdW, parameter 'a' is the speed of mean reversion and 'b' is the long-run mean. High rates (r > b) → drift term is negative → rates tend to fall. B is correct. A is wrong — mean reversion provides a long-run equilibrium. C is wrong — rates don't guarantee return. D is wrong — not oscillatory around zero.
Question 355
The 'Ho-Lee model' for the term structure of interest rates:
Select an option first.
Correct answer: B — Is the simplest no-arbitrage model where the short rate follows: dr = θ(t)dt + σdW — only drift is time-dependent, fitting today's yield curve exactly but allowing negative rates
Explanation: B is correct: the Ho-Lee model was the first no-arbitrage short-rate model. It uses a time-varying drift θ(t) calibrated to exactly match today's yield curve, with constant volatility σ. It is the simplest form but has no mean reversion and allows negative rates. It was later extended by Hull-White (adding mean reversion). A is wrong — Ho-Lee is a one-factor model. C is wrong — no lognormal constraint. D is wrong — Ho-Lee has no mean reversion.
Question 356
Under SOFR transition for derivatives, the key challenge compared to LIBOR is:
Select an option first.
Correct answer: B — SOFR is an overnight (backward-looking) secured rate without a built-in term structure or credit spread — term rates and credit spread adjustments were needed for legacy LIBOR instruments
Explanation: B is correct: LIBOR provided term rates (1M, 3M, 6M) with credit spreads. SOFR is originally overnight and risk-free (secured). Challenges include: building term SOFR (forward-looking); determining appropriate spread adjustments for legacy LIBOR contracts; and adapting documentation. The Alternative Reference Rate Committee (ARRC) developed conventions and spread adjustments to facilitate transition. A is wrong — LIBOR was a term rate; SOFR is overnight (though term SOFR now exists). C is wrong — SOFR is generally smoother than LIBOR. D is wrong — SOFR applies to swaps.
Question 357
For a bond with embedded options, the 'effective convexity' measure:
Select an option first.
Correct answer: B — Accounts for changes in expected cash flows (prepayments/calls) as rates change — calculated as (P+ + P− − 2P₀) / (P₀ × (Δy)²) using an option model to price at each yield level
Explanation: B is correct: effective convexity uses option-adjusted bond prices at parallel yield shifts (+Δy and -Δy) to capture the non-linearity of price changes including embedded option effects. For callable bonds, this produces negative convexity near the call boundary. The formula is: C_eff = (P₊ + P₋ − 2P₀) / (P₀ × (Δy)²). A is wrong — that ignores embedded options. C is wrong — effective convexity differs when options affect cash flows. D is wrong — it is measured using option models.
Question 358
The 'benchmark spread' on a corporate bond (often called the G-spread) represents:
Select an option first.
Correct answer: B — The yield difference between the corporate bond and an on-the-run government bond of similar maturity — a rough but widely-used credit/liquidity spread measure
Explanation: B is correct: the G-spread (government spread) = YTM(corporate) − YTM(comparable Treasury). It is the most straightforward spread measure, using the yield of the nearest-maturity Treasury bond. The I-spread uses interpolated government yields; the Z-spread uses the full spot curve. A is wrong — bid-ask spread is a transaction cost. C is wrong — YTM vs coupon is the coupon effect. D is wrong — ratings are ordinal, not numerical spreads.
Question 359
In structured finance, a 'tranche' represents:
Select an option first.
Correct answer: B — A portion of a structured product with a specific payment priority, risk profile, and credit rating — designed to meet the requirements of different investors with different risk appetites
Explanation: B is correct: tranching allows a single pool of assets to support multiple classes of securities with different risk profiles. Senior tranches (AAA) receive payments first and absorb losses last; junior/equity tranches receive payments last but absorb losses first. This allows the structure to create higher-rated securities from lower-rated collateral through credit enhancement. A is wrong — tranches have different priorities. C is wrong — documentation is the legal agreement. D is wrong — the pool is the collateral, not a tranche.
Question 360
The 'gamma' of an at-the-money (ATM) option compared to deep in-the-money (ITM) or out-of-the-money (OTM) options is:
Select an option first.
Correct answer: B — Highest for ATM options — the delta of an ATM option changes most rapidly with underlying price movements (maximum curvature at ATM)
Explanation: B is correct: gamma is the rate of change of delta. For ATM options, a small change in the underlying price changes the likelihood of expiring ITM most significantly, making delta the most sensitive. Deep ITM options have delta near 1 (insensitive); deep OTM options have delta near 0 (also insensitive). The curvature (gamma) peaks at ATM. A is wrong — ATM has highest gamma. C is wrong — gamma varies significantly with moneyness. D is wrong — deep ITM options have low gamma.
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