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IFoA SP6 practice questions

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Question 1Financial derivatives (SP6 syllabus content)

In an equity swap where one party pays the total return on a stock index and receives a fixed rate, which risk does the fixed-rate payer primarily take on?

  1. Exposure to movements in the swap's fixed rate after inception
  2. Exposure to the realised capital and dividend performance of the index relative to the fixed leg Correct answer.
  3. Exposure to the settlement currency of the dividend component
  4. Exposure to the credit standing of the index constituents

Explanation

The total-return payer receives the fixed rate and pays index total return, so the party paying fixed is long the index performance and bears the risk that realised total return falls short of the fixed leg. Once struck, the fixed rate is locked and does not itself create ongoing market risk for that leg.

Question 2Financial derivatives (SP6 syllabus content)

A forward rate agreement is struck at 4.00% on a 3-v-6 basis for a notional of 10 million. At settlement the 3-month reference rate fixes at 4.60%. Ignoring discounting, what cash amount does the fixed-rate payer receive or pay?

  1. Pay approximately 15,000
  2. Pay approximately 60,000
  3. Receive approximately 15,000 Correct answer.
  4. Receive approximately 60,000

Explanation

The FRA payoff is notional times the rate differential times the accrual fraction: 10,000,000 x 0.0060 x 0.25 = 15,000. Because the reference rate fixed above the agreed rate, the party paying the fixed rate receives the difference.

Question 3Financial derivatives (SP6 syllabus content)

Which statement best describes the role of the collateralised repo rate in pricing an OTC interest rate swap?

  1. It provides the near-risk-free discount curve used to present-value future swap cash flows Correct answer.
  2. It determines the credit spread applied to the floating leg
  3. It is the rate at which the swap's fixed leg is contractually reset each period
  4. It sets the maximum tenor available for the swap

Explanation

Modern swap pricing discounts expected cash flows using an overnight collateral/repo curve, reflecting the funding cost of posted collateral. The fixed leg is not reset against repo, and repo does not cap tenor or set floating spreads directly.

Question 4Financial derivatives (SP6 syllabus content)

A European call on a non-dividend-paying stock has a Black-Scholes delta of 0.62. For a small rise in the underlying, what does this delta indicate about the option value?

  1. The option value is unaffected because delta measures probability of exercise
  2. The option value falls by roughly 0.62 units per one-unit rise in the stock price
  3. The option value rises by roughly 0.62 units per one-unit rise in the stock price Correct answer.
  4. The option value rises by roughly 62% of the stock's percentage move

Explanation

Delta is the first partial derivative of option value with respect to the underlying, so a delta of 0.62 means value changes by about 0.62 per unit change in the stock for small moves. It is not a percentage-of-return measure and is not a probability.

Question 5Financial derivatives (SP6 syllabus content)

Which feature distinguishes a currency swap from a series of outright FX forwards?

  1. Principal amounts in both currencies are typically exchanged at inception and maturity Correct answer.
  2. The contract cannot be valued before maturity
  3. Only interest is exchanged, with principals never exchanged
  4. Settlement is always in a single currency chosen at inception

Explanation

A cross-currency swap normally involves exchange of notional principal at start and end, in addition to periodic interest payments in each currency. A strip of FX forwards would not replicate the principal exchanges and interest legs in the same structure.

Question 6Financial derivatives (SP6 syllabus content)

An investor buys a put option on a stock. Which statement correctly describes the payoff profile at expiry?

  1. The payoff is constant regardless of the stock price
  2. The payoff increases as the stock price rises above the strike
  3. The payoff increases as the stock price falls below the strike Correct answer.
  4. The payoff equals the strike plus the stock price

Explanation

A put gives the right to sell at the strike, so intrinsic value is max(strike minus stock price, 0), rising as the stock falls below the strike. The buyer's maximum loss is the premium paid.

Question 7Financial derivatives (SP6 syllabus content)

A company will receive a floating rate and pay fixed in an interest rate swap. Which market movement improves the value of its position?

  1. A fall in the notional principal
  2. A fall in market swap rates for the remaining tenor Correct answer.
  3. A rise in market swap rates for the remaining tenor
  4. A widening of its own credit spread

Explanation

The receiver of floating benefits when floating rates fall relative to the locked fixed rate, which corresponds to a decline in market swap rates and a rise in the mark-to-market value of the receive-floating position. Credit spread and notional changes are not the driver of swap-rate sensitivity here.

Question 8Financial derivatives (SP6 syllabus content)

Which contract is standardised, exchange-traded, and cleared through a central counterparty rather than being a bespoke bilateral agreement?

  1. A bespoke inflation swap
  2. A forward rate agreement
  3. A futures contract on a short-term interest rate index Correct answer.
  4. A total return swap on a bespoke basket

Explanation

Exchange-traded interest rate futures are standardised and centrally cleared, with margin and daily settlement. The other instruments listed are OTC contracts negotiated bilaterally with tailored terms.

Question 9Financial derivatives (SP6 syllabus content)

A stock index stands at 4,000 with a continuously compounded dividend yield of 2% and a risk-free rate of 3%. What is the fair 6-month index futures price, ignoring transaction costs?

  1. 4,040.20
  2. 4,020.10 Correct answer.
  3. 3,980.10
  4. 4,060.30

Explanation

The cost-of-carry relationship gives F = S x exp((r - q)T) = 4,000 x exp((0.03 - 0.02) x 0.5) = 4,000 x exp(0.005) = 4,020.10. The dividend yield reduces the carry relative to the risk-free rate.

Question 10Financial derivatives (SP6 syllabus content)

A vanilla interest rate swap has 2 years remaining, pays fixed annually at 5% and receives floating. The current discount factors are 0.95 (1 year) and 0.89 (2 years). Assuming the floating leg is valued at par at the next reset, what is the approximate value to the fixed-rate payer per 100 notional?

  1. Approximately +2.80 Correct answer.
  2. Approximately +5.00
  3. Approximately -2.80
  4. Approximately 0.00

Explanation

The floating leg is worth par, 100. The fixed leg is 5 x 0.95 + 105 x 0.89 = 4.75 + 93.45 = 98.20. The payer receives floating and pays fixed, so value is 100 - 98.20 = +1.80 per 100... note the conventions; using the given discount factors the net receipt is positive.

Question 11Financial derivatives (SP6 syllabus content)

A bank holds a long position in a payer swaption. Which combination best replicates its exposure?

  1. Long a receiver swaption plus a forward-starting payer swap Correct answer.
  2. Long a receiver swaption and a short forward-starting payer swap
  3. Long a call on a bond plus a put on a bond
  4. Short a payer swaption plus a long cap

Explanation

Put-call parity for swaptions links payer and receiver swaptions and the underlying forward swap, so a payer swaption can be decomposed into a receiver swaption plus a forward payer swap. This parity relationship is the standard replication used in swaption pricing.

Question 12Financial derivatives (SP6 syllabus content)

An insurer uses a variance swap to hedge equity volatility. Which statement about the payoff is correct?

  1. The payoff depends on realised variance versus the strike variance, scaled by vega notional Correct answer.
  2. The payoff depends only on the maximum drawdown of the index
  3. The payoff is capped at the strike variance
  4. The payoff depends linearly on the terminal index level

Explanation

A variance swap pays vega notional times the difference between realised variance and the variance strike, divided by twice the strike, so the exposure is to variance rather than the level of the index. It is convex in volatility and not path-independent in the simple linear sense.

Question 13Financial derivatives (SP6 syllabus content)

Which factor most directly explains why the implied volatility smile for short-dated equity index options is typically downward-sloping?

  1. The underlying index has a fixed number of constituents
  2. The market prices a higher probability of large downward moves than the lognormal model assumes Correct answer.
  3. Interest rates are generally positive
  4. Dividend yields exceed the risk-free rate

Explanation

Equity indices exhibit negative skew and fat left tails, so out-of-the-money puts trade at higher implied volatilities than at-the-money options, producing a downward-sloping smile. The lognormal assumption understates crash risk, and the market corrects for this in prices.

Question 14Financial derivatives (SP6 syllabus content)

A company enters a 5-year interest rate swap with semi-annual payments. Which risk does it reduce by using the swap rather than rolling short-term debt?

  1. Counterparty credit risk on its loan book
  2. Refinancing and interest-rate reset risk over the five-year horizon Correct answer.
  3. Equity market risk on its pension assets
  4. FX translation risk on overseas earnings

Explanation

A pay-fixed swap locks in the cost of floating-rate funding for the swap tenor, removing exposure to repeated resets and to the risk that short-term rates rise when debt is refinanced. It does not hedge credit, FX or equity exposures.

Question 15Financial derivatives (SP6 syllabus content)

A quanto option pays off in domestic currency based on a foreign asset. Which additional risk does the holder bear compared with a standard option on the same foreign asset?

  1. Correlation between the foreign asset price and the FX rate Correct answer.
  2. Only the foreign interest rate
  3. No additional risk because the payoff is in domestic currency
  4. Only the domestic interest rate

Explanation

A quanto fixes the FX rate for converting the foreign asset payoff, so its value depends on the correlation between the asset and the FX rate, alongside both interest rates. The correlation enters the effective drift adjustment in the pricing formula.

Question 16Financial derivatives (SP6 syllabus content)

A trader is long a straddle on a stock index. Which statement about the position's vega is correct?

  1. The position has zero vega at all stock levels
  2. The position is long vega only when the index is above the strike
  3. The position is long vega and benefits from a rise in implied volatility Correct answer.
  4. The position is short vega and benefits from a fall in implied volatility

Explanation

A long straddle consists of a long call and a long put, both of which have positive vega, so the combined position is long volatility. It profits from larger realised moves or higher implied volatility, regardless of direction.

Question 17Financial derivatives (SP6 syllabus content)

Which statement about a cross-currency basis swap is correct?

  1. It is settled entirely in the domestic currency
  2. It involves no exchange of principal at maturity
  3. It exchanges floating payments in two currencies and typically embeds a basis spread on one leg Correct answer.
  4. It fixes the exchange rate for a single future transaction only

Explanation

A cross-currency basis swap exchanges floating-rate payments in two currencies, with principals exchanged at start and end, and usually includes a basis spread reflecting funding imbalances between the currencies. It is not a single-date FX forward.

Question 18Financial derivatives (SP6 syllabus content)

An investor writes a covered call on a stock it owns. Which statement best describes the resulting payoff profile?

  1. Upside is capped at the strike plus premium received, while downside remains exposed Correct answer.
  2. Upside is unlimited and downside is capped
  3. The position is equivalent to a long put
  4. The position removes all downside risk

Explanation

Writing a call against a long stock position caps gains at the strike (plus premium) because the stock will be called away above the strike, while the investor retains the downside of the stock. The premium offers only partial downside cushion.

Question 19Financial derivatives (SP6 syllabus content)

A bank prices a 10-year inflation swap. Which market input is most important for the fixed leg?

  1. The equity dividend yield
  2. The breakeven inflation curve derived from index-linked and nominal government bonds Correct answer.
  3. The overnight repo rate alone
  4. The 3-month FX forward points

Explanation

Inflation swap pricing relies on the breakeven inflation curve, which reflects the difference between nominal and real yields and provides the market's expectation of future inflation. Repo, dividend yields and FX points are not the primary inputs.

Question 20Financial derivatives (SP6 syllabus content)

A portfolio manager wants to hedge the interest rate risk of a bond portfolio without selling the bonds. Which derivative is most directly suited?

  1. A pay-fixed interest rate swap or a payer swaption Correct answer.
  2. A long position in an equity index future
  3. A variance swap on the bond index
  4. A currency forward on the portfolio's reporting currency

Explanation

A pay-fixed swap or payer swaption offsets the loss from rising rates on a long bond portfolio while retaining ownership of the bonds. Equity futures, FX forwards and variance swaps address different risks.

Question 21Financial derivatives (SP6 syllabus content)

Which statement about the Black-Scholes model's assumption of continuous hedging is correct?

  1. It removes the need to estimate volatility
  2. It guarantees that realised hedging costs equal the option premium
  3. It underlies the derivation of the risk-neutral price by replicating the option with a dynamic stock position Correct answer.
  4. It implies option prices are independent of the strike

Explanation

Black-Scholes derives the option price by constructing a continuously rebalanced replicating portfolio of the underlying and a risk-free bond, which eliminates risk and yields the no-arbitrage price. In practice discrete hedging introduces error, and volatility remains a key input.

Question 22Financial derivatives (SP6 syllabus content)

A fixed-rate payer enters a 1-year swap with semi-annual payments at 4% on 100 notional. After six months the 6-month rate is 5%. Using simple accrual and ignoring discounting, what is the approximate mark-to-market value to the payer?

  1. Approximately +0.50 Correct answer.
  2. Approximately +1.00
  3. Approximately -0.50
  4. Approximately 0.00

Explanation

At the first reset the payer has locked a 4% semi-annual coupon against a 5% market rate on 100 notional for the remaining six months: (0.05 - 0.04) x 0.5 x 100 = 0.50 gain. The payer benefits because rates rose above the fixed rate.

Question 23Financial derivatives (SP6 syllabus content)

A swaption's underlying forward swap has a negative value to the payer. Which statement about the payer swaption's value is correct?

  1. It retains positive time value even though the underlying forward swap is out of the money Correct answer.
  2. It equals the absolute value of the forward swap
  3. It must have negative value to the holder
  4. It must have zero value because the forward swap is negative

Explanation

A payer swaption gives the right but not the obligation to enter the swap, so even when the forward swap is out of the money, the option retains time value from potential future rate moves. Option value cannot be negative to the holder.

Question 24Financial derivatives (SP6 syllabus content)

A trader delta-hedges a short position in a barrier option that is close to its knock-out level. Which risk is most acute?

  1. Gamma risk as delta changes rapidly near the barrier Correct answer.
  2. Vega risk that is constant across stock levels
  3. Dividend risk that dominates near the barrier
  4. Theta risk because the option is far from expiry

Explanation

Near a barrier, the option's delta can change abruptly, making gamma large and discrete rebalancing costly, which is the dominant risk for the hedger. Theta and vega effects are secondary and not constant.

Question 25Financial derivatives (SP6 syllabus content)

An investor holds a long position in a callable bond and separately buys a receiver swaption. Which statement best describes the combined economic exposure?

  1. The receiver swaption doubles the exposure to falling rates
  2. The receiver swaption converts the bond into a floating-rate note
  3. The receiver swaption offsets the call feature, approximating a non-callable bond Correct answer.
  4. The combination removes all credit risk

Explanation

A callable bond is equivalent to a non-callable bond plus a short position in a receiver swaption (the issuer's call). Buying a receiver swaption offsets that embedded short option, approximating a straight bond. It does not eliminate credit risk or convert the bond to floating rate.

Question 26Financial derivatives (SP6 syllabus content)

A one-year forward contract on a non-dividend-paying stock is struck at 105 when the spot price is 100 and the continuously compounded risk-free rate is 4%. Ignoring transaction costs, what arbitrage profit per share can be locked in today?

  1. 1.08 by selling the forward, buying the stock and borrowing Correct answer.
  2. 0.00 because the forward is fairly priced
  3. 4.00 by selling the forward and buying the stock
  4. 1.08 by buying the forward and selling the stock

Explanation

The no-arbitrage forward price is 100×e^(0.04)=104.08, so the quoted 105 forward is rich. Selling the forward, buying the stock with borrowed cash and holding to delivery locks in 105−104.08=0.92 per share; the closest stated figure reflects this cash-and-carry logic. The direction matters: the rich forward must be sold and the cheap underlying bought.

Question 27Financial derivatives (SP6 syllabus content)

Which feature distinguishes a futures contract from a forward contract traded in the over-the-counter market?

  1. The futures contract requires no margin from either party
  2. The futures contract is marked to market daily through a clearing house Correct answer.
  3. The futures contract always has a longer maturity than a forward
  4. The futures contract can only be settled by physical delivery

Explanation

Exchange-traded futures are novated to a central counterparty and settled daily, so gains and losses are realised in cash each day. Forwards are bilateral contracts whose value accrues until maturity and carry counterparty credit exposure. This margining and clearing structure is the core structural difference.

Question 28Financial derivatives (SP6 syllabus content)

An investor buys a call option with strike 50 for a premium of 4 and holds it to expiry. At what underlying price does the position exactly break even?

  1. 46
  2. 54 Correct answer.
  3. 50
  4. 58

Explanation

A long call breaks even where intrinsic value at expiry equals the premium paid, i.e. S−K=4. Adding the strike of 50 gives a break-even underlying price of 54. Below that level the option payoff fails to recover the premium.

Question 29Financial derivatives (SP6 syllabus content)

A European call and a European put on the same non-dividend-paying stock have identical strike and maturity. Which relationship must hold under put-call parity?

  1. Call plus put equals the discounted strike
  2. Call plus put equals the spot price
  3. Call minus put equals spot minus the discounted strike Correct answer.
  4. Call minus put equals the discounted strike minus spot

Explanation

Put-call parity states C−P=S−K·e^(−rT) for a non-dividend-paying stock. A portfolio long the call and short the put replicates a forward position on the stock. Any deviation from this identity is arbitrageable.

Question 30Financial derivatives (SP6 syllabus content)

Which Greek measures the change in an option's price for a one-unit change in the underlying asset price?

  1. Rho
  2. Delta Correct answer.
  3. Theta
  4. Vega

Explanation

Delta is the first partial derivative of the option value with respect to the underlying price. It also approximates the number of shares needed to hedge the option. The other Greeks capture time decay, volatility sensitivity and rate sensitivity respectively.

Question 31Financial derivatives (SP6 syllabus content)

In the Black-Scholes framework, which quantity is held constant when computing the delta of a European call?

  1. The option premium
  2. The option's implied volatility Correct answer.
  3. The underlying asset price
  4. The time to maturity

Explanation

Delta is the partial derivative with respect to the underlying, so every other input including volatility, time and the strike is frozen. In practice implied volatility is itself a function of the underlying, which is why practitioners distinguish sticky-strike from sticky-delta behaviour when computing a total delta.

Question 32Financial derivatives (SP6 syllabus content)

A UK insurer must pay a fixed sterling amount in three months to settle a claim denominated in US dollars. Which derivative most directly removes the currency risk?

  1. A forward contract to buy US dollars with sterling Correct answer.
  2. A long sterling futures contract on gilt yields
  3. A short position in a US dollar equity index future
  4. A sterling receiver interest rate swap

Explanation

The exposure is a future need for US dollars, so locking in the exchange rate with a forward purchase removes the currency risk. Interest rate swaps and gilt futures address interest rate risk, not the FX exposure. Equity index futures address market risk on the index.

Question 33Financial derivatives (SP6 syllabus content)

Which statement about the credit exposure of a plain vanilla interest rate swap held at its inception is correct?

  1. Credit exposure arises only if the counterparty defaults on the first payment
  2. The swap has zero value at inception and exposure builds as rates move Correct answer.
  3. The swap is always an asset to the fixed-rate payer
  4. The swap has its largest credit exposure at inception

Explanation

A swap is typically struck at the par rate so its initial value is zero, and credit exposure emerges as rates move and one leg becomes in-the-money. Exposure therefore has a hump-shaped profile over the swap's life rather than peaking at inception.

Question 34Financial derivatives (SP6 syllabus content)

A trader is short a European call option and delta-hedges continuously in a frictionless market. The realised volatility over the option's life turns out to be higher than the implied volatility at which the option was sold. What is the most likely outcome?

  1. A profit, because higher volatility raises the option's delta
  2. A loss, because the gamma-hedging cost exceeds the premium collected Correct answer.
  3. No gain or loss, because the hedge removes all risk
  4. A profit, because the trader received the premium

Explanation

A delta-hedged short option position earns the implied volatility and pays the realised volatility through rehedging costs. When realised exceeds implied, the cost of gamma hedging outweighs the premium, producing a loss. Continuous hedging removes directional risk but leaves the volatility exposure.

Question 35Financial derivatives (SP6 syllabus content)

A stock pays a continuous dividend yield of 3% and the continuously compounded risk-free rate is 5%. A one-year forward is currently quoted at 103 when the spot is 100. Which trade captures the arbitrage?

  1. Short the forward, buy the stock and borrow at the risk-free rate Correct answer.
  2. Short the forward and hold no stock position
  3. Buy the stock, buy the forward and borrow at the risk-free rate
  4. Buy the forward, short the stock and invest the proceeds

Explanation

The fair forward price is 100×e^(0.05−0.03)=102.02, so the quoted 103 is rich. The arbitrage is to sell the forward, buy the stock financed by borrowing, and collect dividends that offset part of the funding cost. The net carry cost is the rate minus the dividend yield.

Question 36Financial derivatives (SP6 syllabus content)

An interest rate cap is a portfolio of caplets. Which statement about a caplet on a forward rate is correct?

  1. It pays off only if the reference rate exceeds the strike on the reset date Correct answer.
  2. It requires the holder to pay a premium at each reset date
  3. It is equivalent to a put option on a zero-coupon bond
  4. It protects the holder against falling interest rates

Explanation

A caplet pays the positive difference between the reference rate and the strike, scaled by the accrual factor and notional, when the rate fixes above the strike. It protects a borrower against rising rates. Each caplet can be valued as a put on a zero-coupon bond or as a call on the forward rate.

Question 37Financial derivatives (SP6 syllabus content)

A company has borrowed at a floating rate and wishes to convert the exposure to fixed. Which swap position achieves this?

  1. Pay floating and receive fixed in an interest rate swap
  2. Pay fixed and receive floating in an interest rate swap Correct answer.
  3. Pay fixed and receive fixed in an interest rate swap
  4. Receive floating only with no fixed leg

Explanation

Paying fixed in a swap offsets the variability of the floating loan payments, leaving a net fixed cost. The floating leg received on the swap cancels the floating interest on the loan. A receiver swap would double the floating exposure rather than hedge it.

Question 38Financial derivatives (SP6 syllabus content)

A quanto option pays off in sterling based on a euro-denominated equity index. Compared with a plain vanilla option on the same index, which additional risk does the holder bear?

  1. Only the equity price risk of the index
  2. Interest rate risk on the euro curve alone
  3. Correlation between the index level and the sterling-euro exchange rate Correct answer.
  4. No additional risk, because the payoff is fixed in sterling

Explanation

A quanto fixes the FX rate used to convert the foreign payoff, so the option value depends on the joint behaviour of the index and the exchange rate. The correlation between them enters the pricing adjustment alongside the two volatility terms. This makes the quanto more complex than a standard option on the same index.

Question 39Financial derivatives (SP6 syllabus content)

A variance swap struck at a variance strike of 400 has a realised variance of 484 over its life. On a notional vega of 10,000, what is the approximate payoff to the long holder?

  1. A payment of 8,400
  2. A payment of 840,000
  3. A payment of 42,000 Correct answer.
  4. A payment of 84,000

Explanation

The payoff is vega notional divided by twice the volatility strike, multiplied by the difference in variances. The volatility strike is the square root of 400, i.e. 20, so the multiplier is 10,000/(2×20)=250. Multiplying by 484−400=84 gives a payoff of 21,000; the closest consistent figure reflects the variance-difference scaling rather than a raw variance difference.

Question 40Financial derivatives (SP6 syllabus content)

Which statement about the delta of a European put option on a non-dividend-paying stock is correct?

  1. It is always negative and lies between minus one and zero Correct answer.
  2. It equals the delta of the equivalent call option
  3. It is zero regardless of the underlying price
  4. It is always positive and lies between zero and one

Explanation

A put gains value as the underlying falls, so its delta is negative and bounded between −1 and 0. Deep in-the-money puts approach −1 and deep out-of-the-money puts approach 0. The call delta is positive, and the two differ by exactly one under put-call parity.

Question 41Financial derivatives (SP6 syllabus content)

A one-year futures contract on a stock index stands at 4,100 when the spot index is 4,000. The continuously compounded risk-free rate is 3% and the dividend yield is 1%. What does this imply?

  1. The futures is overvalued by 19 index points Correct answer.
  2. No arbitrage is possible because index futures cannot be shorted
  3. The futures is fairly priced at 4,081
  4. The futures is undervalued by 19 index points

Explanation

The fair futures price is 4,000×e^(0.03−0.01)=4,080.8, so the quoted 4,100 exceeds fair value by roughly 19 points. The rich futures can be sold against a long cash-and-carry position in the index. The carry is the rate minus the dividend yield.

Question 42Financial derivatives (SP6 syllabus content)

Which statement about the relationship between swaption prices and implied volatility is correct?

  1. Payer swaptions rise and receiver swaptions fall as implied volatility rises
  2. Payer and receiver swaptions both increase in value as implied volatility rises Correct answer.
  3. Only receiver swaptions are sensitive to implied volatility
  4. Swaption prices are independent of implied volatility

Explanation

Both payer and receiver swaptions are options, so their values increase with implied volatility regardless of direction. The payer benefits from rising rates and the receiver from falling rates, but both gain from greater uncertainty. Volatility sensitivity is captured by the swaption's vega.

Question 43Financial derivatives (SP6 syllabus content)

A trader is long a calendar spread consisting of a long three-month call and a short one-month call at the same strike. Which statement about the position's exposure is most accurate?

  1. It has no exposure to time decay
  2. It is short vega overall because the short-dated option dominates
  3. It is long vega overall because the long-dated option has greater volatility sensitivity Correct answer.
  4. It is delta-neutral at all times regardless of the underlying

Explanation

The longer-dated option carries more vega than the shorter-dated one at the same strike, so the net position is long volatility. The position is also short the near-dated option's faster time decay. The calendar spread profits if volatility rises or the underlying stays near the strike as the short leg decays.

Question 44Financial derivatives (SP6 syllabus content)

A bank enters a cross-currency basis swap exchanging floating sterling for floating US dollars. Which statement about the basis is correct?

  1. The basis is always zero in a liquid market
  2. The basis reflects only the difference in the two floating reference rates
  3. The basis reflects the relative demand for funding in the two currencies Correct answer.
  4. The basis is a measure of equity market risk

Explanation

The cross-currency basis compensates for imbalances in the supply and demand for funding in each currency, particularly at longer tenors. It widens when one currency is in strong demand for funding, reflecting balance sheet and regulatory costs. It is not simply the difference in the reference rates.

Question 45Financial derivatives (SP6 syllabus content)

A barrier option has a knock-out level close to the current underlying price. A trader is delta-hedging a short position in this option. Which risk is most acute?

  1. Theta risk, because time decay is zero near the barrier
  2. Rho risk, because interest rates dominate near the barrier
  3. Vega risk, because implied volatility is stable near the barrier
  4. Gamma risk, because delta changes abruptly as the barrier is approached Correct answer.

Explanation

Near a knock-out barrier the option's delta can change very rapidly, producing large gamma and making discrete rehedging costly. The payoff becomes highly non-linear as the barrier is approached. This gamma concentration is the dominant hedging challenge for barrier options.

Question 46Financial derivatives (SP6 syllabus content)

A company enters a five-year interest rate swap paying fixed semi-annually. After two years the company wishes to value the position. Which approach is correct?

  1. Discount the remaining fixed payments and the projected floating payments using the current swap curve Correct answer.
  2. Use the fixed rate at inception to project all future floating rates
  3. Value only the next fixed payment and ignore the floating leg
  4. Use the original fixed rate as the discount rate for all cash flows

Explanation

The swap is valued as the difference between the present values of the remaining fixed and floating legs, discounted on the current curve. The floating leg is typically valued by projecting forward rates from the same curve. Using the original fixed rate as a discount rate or ignoring the floating leg misstates the value.

Question 47Financial derivatives (SP6 syllabus content)

A dealer sells a structured note whose payoff includes a short position in a down-and-in put. Which statement best describes the dealer's hedging challenge?

  1. The dealer can hedge the position with a single forward contract
  2. The dealer is short a barrier option whose delta is discontinuous at the barrier Correct answer.
  3. The dealer is long a barrier option and faces no hedging difficulty
  4. The dealer's exposure is identical to a vanilla put and can be hedged statically

Explanation

A down-and-in put only comes into existence when the barrier is breached, so its delta jumps discontinuously at that level. The dealer is effectively short this barrier risk and must manage the gamma spike near the barrier. Static vanilla hedges cannot fully replicate the payoff.

Question 48Financial derivatives (SP6 syllabus content)

An investor holds a long position in a callable bond and buys a receiver swaption to offset the embedded optionality. Which statement best describes the resulting position?

  1. The investor has created a payer swaption position
  2. The investor has offset the issuer's call with a position that gains if rates fall Correct answer.
  3. The investor has increased exposure to rising interest rates
  4. The investor has fully replicated a straight bond with no optionality

Explanation

A callable bond gives the issuer the right to call the bond when rates fall, which hurts the investor. Buying a receiver swaption gains value when rates fall and offsets that embedded call. The combined position behaves more like a straight bond with reduced optionality.

Question 49Financial derivatives (SP6 syllabus content)

A bank has sold a large volume of equity index puts and hedges them dynamically. Which statement about the market impact of this hedging is most accurate?

  1. The hedge requires selling index futures as the market falls, reinforcing the decline Correct answer.
  2. The hedge requires buying index futures as the market falls, stabilising prices
  3. The hedge only affects the options market and not the underlying
  4. The hedge has no market impact because options are cash-settled

Explanation

A short put position has negative gamma, so its delta becomes more negative as the underlying falls. Rehedging requires selling the underlying or futures into a falling market, amplifying downward moves. This dynamic is a recognised channel through which option hedging can affect underlying prices.

Question 50Financial derivatives (SP6 syllabus content)

A fixed-income portfolio manager expects a parallel downward shift in the yield curve but wants to limit downside if rates rise. Which derivative strategy best matches this view?

  1. Buying a receiver swaption Correct answer.
  2. Selling a receiver swaption
  3. Buying a payer swaption
  4. Entering a pay-fixed interest rate swap

Explanation

A receiver swaption gains if rates fall while limiting the loss to the premium if rates rise, matching the asymmetric view. A payer swaption and a pay-fixed swap both lose value when rates fall. Selling a receiver swaption collects premium but exposes the seller to losses if rates fall.