Financial Engineering
Test Bank
Course Introduction
Financial Engineering is a multidisciplinary field that applies mathematical methods, computational tools, and financial theory to analyze and solve complex problems in finance. The course explores topics such as derivative pricing, risk management, portfolio optimization, and structured products, integrating concepts from probability, statistics, economics, and computer science. Students will learn to design and implement innovative financial instruments and strategies, utilize quantitative models for asset valuation, and develop skills in managing financial risk in uncertain markets. Emphasis is placed on practical applications, real-world case studies, and the use of software tools for modeling and simulation in modern financial markets.
Recommended Textbook Fundamentals of Futures and Options Markets 8th Edition by John C. Hull
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Chapter 1: Introduction
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Q1) A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contract trade on the index with one contract being on 250 times the index. To remove market risk from the portfolio the trader should
A) Buy 16 contracts
B) Sell 16 contracts
C) Buy 20 contracts
D) Sell 20 contracts
Answer: B
Q2) The price of a stock on July 1 is $57. A trader buys 100 call options on the stock with a strike price of $60 when the option price is $2. The options are exercised when the stock price is $65. The trader's net profit is
A) $700
B) $500
C) $300
D) $600
Answer: C
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Chapter 2: Mechanics of Futures Markets
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Q1) You sell one December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you provide is $2,000. The maintenance margin per contract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day?
A) $1,800
B) $3,300
C) $2,200
D) $3,700
Answer: A
Q2) Which entity in the United States takes primary responsibility for regulating futures market?
A) Federal Reserve Board
B) Commodities Futures Trading Commission (CFTC)
C) Security and Exchange Commission (SEC)
D) US Treasury
Answer: B
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Chapter 3: Hedging Strategies Using Futures
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Q1) A silver mining company has used futures markets to hedge the price it will receive for everything it will produce over the next 5 years. Which of the following is true?
A) It is liable to experience liquidity problems if the price of silver falls dramatically
B) It is liable to experience liquidity problems if the price of silver rises dramatically
C) It is liable to experience liquidity problems if the price of silver rises dramatically or falls dramatically
D) The operation of futures markets protects it from liquidity problems
Answer: B
Q2) Which of the following best describes the capital asset pricing model?
A) Determines the amount of capital that is needed in particular situations
B) Is used to determine the price of futures contracts
C) Relates the return on an asset to the return on a stock index
D) Is used to determine the volatility of a stock index
Answer: C
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Chapter 4: Interest Rates
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Q1) An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?
A) 5.06%
B) 5.03%
C) 4.97%
D) 4.94%
Q2) The six-month zero rate is 8% per annum with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?
A) 8.02%
B) 8.52%
C) 9.02%
D) 9.52%
Q3) Which of the following is true of LIBOR?
A) The LIBOR rate is free of credit risk
B) A LIBOR rate is lower than the Treasury rate when the two have the same maturity
C) It is a rate used when borrowing and lending takes place between banks
D) It is subject to favorable tax treatment in the U.S.
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Chapter 5: Determination of Forward and Futures Prices
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Q1) Which of the following describes the way the futures price of a foreign currency is quoted?
A) The number of U.S. dollars per unit of the foreign currency
B) The number of the foreign currency per U.S. dollar
C) Some futures prices are always quoted as the number of U.S. dollars per unit of the foreign currency and some are always quoted the other way round
D) There are no quotation conventions for futures prices
Q2) A short forward contract that was negotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for three-month forward contract is $42. The three month risk-free interest rate (with continuous compounding) is 8%. What is the value of the short forward contract?
A) +$2.00
B) -$2.00
C) +$1.96
D) -$1.96
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Chapter 6: Interest Rate Futures
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Q1) A portfolio is worth $24,000,000. The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000. On the delivery date the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many contracts are necessary for hedging the portfolio?
A) 100
B) 200
C) 300
D) 400
Q2) A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six months. How many contracts are required?
A) 5
B) 10
C) 15
D) 20
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8
Chapter 7: Swaps
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Q1) Since the 2008 credit crisis
A) LIBOR has replaced OIS as the discount rate for non-collateralized swaps
B) OIS has replaced LIBOR as the discount rate for non-collateralized swaps
C) LIBOR has replaced OIS as the discount rate for collateralized swaps
D) OIS has replaced LIBOR as the discount rate for collateralized swaps
Q2) Which of the following is true?
A) Principals are not usually exchanged in a currency swap
B) The principal amounts usually flow in the opposite direction to interest payments at the beginning of a currency swap and in the same direction as interest payments at the end of the swap
C) The principal amounts usually flow in the same direction as interest payments at the beginning of a currency swap and in the opposite direction to interest payments at the end of the swap
D) Principals are not usually specified in a currency swap
Q3) A floating-for-fixed currency swap is equivalent to
A) Two interest rate swaps, one in each currency
B) A fixed-for-fixed currency swap and one interest rate swap
C) A fixed-for-fixed currency swap and two interest rate swaps, one in each currency
D) None of the above
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following describes a subprime mortgage?
A) The rate of interest is less than the prime rate of interest
B) The loan-to-value ratio is below average
C) The life of the mortgage is less than 25 years
D) The credit risk is high
Q2) Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 94.5% (rated AAA), mezzanine 0.1% (rated BBB), and equity 5% (ratedC). The portfolios of subprime mortgages have the same default rates. An ABS CDO is then created from the mezzanine tranches. Which of the following is true?
A) The ABS CDO tranches should have similar ratings ranging from AAA to C
B) The ABS CDO tranches should all be rated BBB
C) The ABS CDO tranches should all be rated C
D) The ABS CDO tranches are almost worthless because the mezzanine tranches are so thin
Q3) Which of the following would be described by the term "liar loan"?
A) A situation where the lender concealed information from the borrower
B) A situation where the lender lied to the borrower about the interest rate
C) A situation where the borrower lied about his or her income
D) None of the above
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Chapter 9: Mechanics of Options Markets
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Q1) Which of the following describes a long position in an option?
A) A position where there is more than one year to maturity
B) A position where there is more than five years to maturity
C) A position where an option has been purchased
D) A position that has been held for a long time
Q2) Which of the following describes a call option?
A) The right to buy an asset for a certain price
B) The obligation to buy an asset for a certain price
C) The right to sell an asset for a certain price
D) The obligation to sell an asset for a certain price
Q3) Which of the following describes a short position in an option?
A) A position in an option lasting less than one month
B) A position in an option lasting less than three months
C) A position in an option lasting less than six months
D) A position where an option has been sold
Q4) When a six-month option is purchased
A) The price must be paid in full
B) Up to 25% of the option price can be borrowed using a margin account
C) Up to 50% of the option price can be borrowed using a margin account
D) Up to 75% of the option price can be borrowed using a margin account
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Chapter 10: Properties of Stock Options
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Q1) When dividends increases with all else remaining the same, which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
Q2) When the strike price increases with all else remaining the same, which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
Q3) Interest rates are zero. A European call with a strike price of $50 and a maturity of one year is worth $6. A European put with a strike price of $50 and a maturity of one year is worth $7. The current stock price is $49. Which of the following is true?
A) The call price is high relative to the put price
B) The put price is high relative to the call price
C) Both the call and put must be mispriced
D) None of the above
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Page 12
Chapter 11: Trading Strategies Involving Options
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Q1) How can a straddle be created?
A) Buy one call and one put with the same strike price and same expiration date
B) Buy one call and one put with different strike prices and same expiration date
C) Buy one call and two puts with the same strike price and expiration date
D) Buy two calls and one put with the same strike price and expiration date
Q2) When the interest rate is 5% per annum with continuous compounding, which of the following creates a $1000 principal protected note?
A) A one-year zero-coupon bond plus a one-year call option worth about $59
B) A one-year zero-coupon bond plus a one-year call option worth about $49
C) A one-year zero-coupon bond plus a one-year call option worth about $39
D) A one-year zero-coupon bond plus a one-year call option worth about $29
Q3) A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net loss (after the cost of the options is taken into account)?
A) $100
B) $200
C) $300
D) $400
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13
Chapter 12: Introduction to Binomial Trees
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Q1) Which of the following describes delta?
A) The ratio of the option price to the stock price
B) The ratio of the stock price to the option price
C) The ratio of a change in the option price to the corresponding change in the stock price
D) The ratio of a change in the stock price to the corresponding change in the option price
Q2) The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option?
A) $1.6
B) $2.0
C) $2.4
D) $3.0
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14
Chapter 13: Valuing Stock Options: the Bsm Model
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Q1) A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the continuously compounded expected return in one year?
A) 6%
B) 8%
C) 10%
D) 12%
Q2) What is the number of trading days in a year usually assumed for equities?
A) 365
B) 252
C) 262
D) 272
Q3) A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the standard deviation of the change in the stock price in one week?
A) $0.38
B) $2.77
C) $3.02
D) $0.76
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15
Chapter 14: Employee Stock Options
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Q1) Which of the following was true about employee stock options prior to 1995?
A) The options never had any affect on a company's financial statements
B) The value of options which were at-the-money when issued had to be expensed on the income statement
C) The value of options which were at-the-money when issued had to be reported in the notes to the financial statements
D) Options which were at-the-money when issued did not affect a company's financial statements
Q2) Which of the following was true after 2005?
A) The options never had any affect on a company's financial statements
B) The value of options which were at-the-money when issued had to be expensed on the income statement
C) The value of options which were at-the-money when issued had to be reported in the notes to the financial statements
D) Options which were at-the-money when issued did not affect a company's financial statements
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Chapter 15: Options on Stock Indices and Currencies
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Q1) Which of the following is true when a European currency option is valued using forward exchange rates?
A) It is not necessary to know the domestic interest rate or the spot exchange rate
B) It is not necessary to know either the foreign or domestic interest rate
C) It is necessary to know the difference between the foreign and domestic interest rates but not the rates themselves
D) It is not necessary to know the foreign interest rate or the spot exchange rate
Q2) A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. What is the value of the option?
A) 1.11N(0.7)-0.98N(0.5)
B) 1.11N(-0.7)-0.98N(-0.5)
C) 1.11N(0.7)-0.98N(0.4)
D) 1.11N(-0.06)-0.98N(-0.10)
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Chapter 16: Futures Options
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Q1) One-year European call and put options on an asset are worth $3 and $4 respectively when the strike price is $20 and the one-year risk-free rate is 5%. What is the one-year futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.)
A) $19.55
B) $18.95
C) $20.95
D) $20.45
Q2) What is the value of a European call futures option where the futures price is 50, the strike price is 50, the risk-free rate is 5%, the volatility is 20% and the time to maturity is three months?
A) 49.38N(0.05)-49.38N(-0.05)
B) 50N(0.05)-50N(-0.05)
C) 49.38N(0.1)-49.38N(-0.1)
D) 50N(0.1)-49.38N(-0.1)
Q3) Which of the following are true?
A) Futures options are usually European
B) Futures options are usually American
C) Both American and European futures options trade actively are exchanges
D) Both American and European futures options trade actively in the OTC market
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Chapter 17: The Greek Letters
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Q1) A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position should the trader take to hedge the position?
A) Sell 300 shares
B) Buy 300 shares
C) Sell 700 shares
D) Buy 700 shares
Q2) A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of six months. The risk-free rate is 4% and the volatility is 25%. The stock price is $28. What is the delta of the option?
A) N(-0.1342)
B) N(-0.1888)
C) N(-0.2034)
D) N(-0.2241)
Q3) Gamma tends to be high for which of the following?
A) At-the money options
B) Out-of-the money options
C) In-the-money options
D) Options with a long time to maturity
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19
Chapter 18: Binomial Trees in Practice
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Q1) A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black-Scholes price of the European option is $2.98. What is the control variate price of the American option?
A) $3.06
B) $3.18
C) $2.90
D) $3.08
Q2) The chapter discusses an alternative to the Cox, Ross, Rubinstein tree. In this alternative, which of the following are true?
A) The relationship between u and d is: u=1/d
B) The relationship between u and d is: u-1=1-d
C) The probabilities on the tree are all 0.5
D) None of the above
Q3) Which of the following can be valued without using a numerical procedure such as a binomial tree?
A) American put options on a non-dividend paying stock
B) American call options on a non-dividend paying stock
C) American call options on a currency
D) American put options on futures
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Page 20
Chapter 19: Volatility Smiles
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Q1) Which of the following is true when the tails of a future stock price distribution are compared with those of a lognormal distribution with the same mean and standard deviation?
A) The left tail and right tail are thinner
B) The left tail is thinner and the right tail is fatter
C) The right tail is thinner and the left tail is fatter
D) Both tails are fatter
Q2) The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 6 months are 20% and 22%. The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 1 year are 18.8% and 20.2%. Using linear interpolation, what is the implied volatility for a strike price of 1.12 and a time to maturity of 10 months?
A) 19.24%
B) 19.52%
C) 20.48%
D) 19.96%
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21
Chapter 20: Value at Risk
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Q1) At the end of Thursday, the estimated volatility of asset A is 2% per day. During Friday asset A produces a return of 3%. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the volatility of asset A at the end of Friday?
A) 2.08%
B) 2.10%
C) 2.12%
D) 2.14%
Q2) At the end of Thursday, the estimated volatility of asset B is 1% per day. During Friday asset B produces a return of zero. An EWMA model with lambda equal to 0.9 is used. What is an estimate of the volatility of asset A at the end of Friday?
A) 0.98%
B) 0.95%
C) 0.92%
D) 0.90%
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22
Chapter 21: Interest Rate Options
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Q1) A Eurodollar futures option contract has a strike price of 97 and the Eurodollar interest rate is 2.50%. What is the intrinsic value of the contract if the option is a call?
A) $0
B) $1,250
C) $1,750
D) $2,500
Q2) Which of the following is true?
A) A puttable bond allows the lender to ask for the principal to be repaid early
B) A puttable bond allows the borrower to repay the principal early
C) A puttable bond is a bond with an embedded stock option
D) None of the above
Q3) A five-year cap is reset annually period. The cap rate is 3% and the notional principal is $100 million. The 12-month LIBOR interest rate for the third year proves to be 5%. Which of the following is approximately true?
A) The resulting payoff is $2 million at the beginning of the third year
B) The resulting payoff is $2 million at the end of the fifth year
C) The resulting payoff is $2 million at the end of the third year
D) The resulting payoff is $2 million half way through the third year
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Chapter 22: Exotic Options and Other Nonstandard Products
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Q1) Which of the following is equivalent to a short position in a European put option?
A) A short position in a cash-or-nothing put option plus a long position in an asset-or-nothing put option
B) A long position in an asset-or-nothing put option plus a long position in a cash-or-nothing put option
C) A long position in an asset-or-nothing call option plus a long position in a cash-or-nothing call option
D) A long position in an asset-or-nothing call option plus a short position in a cash-or-nothing call option
Q2) An Asian option is a term used to describe which of the following?
A) An option where the payoff depends on whether a barrier is hit
B) An option where the payoff depends on the average value of a variable over a period of time
C) An option that trades on an exchange in the Far East
D) Any option with a nonstandard payoff
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Chapter 23: Credit Derivatives
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Q1) Which of the following happens when the default correlation of the companies underlying a CDO increases?
A) The value of the senior tranche and the equity tranche to the protection buyer both increase
B) The value of the senior tranche and the equity tranche to the protection buyer both decrease
C) The value of the senior tranche to the protection buyer decreases and the value of the equity tranche to the protection buyer increases
D) The value of the senior tranche to the protection buyer increases and the value of the equity tranche to the protection buyer decreases
Q2) A CDS with a number of reference entities provides a payoff when any of the reference entities defaults. What is a name for this CDS?
A) Binary CDS
B) Add-up Basket CDS
C) First-to-Default CDS
D) n-to-Default CDS
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Chapter 24: Weather, Energy, and Insurance Derivatives
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Q1) Which of the following are least likely to use weather derivatives?
A) Energy producers
B) Food and drink manufacturers
C) Companies in the leisure industry
D) Automobile manufacturers
Q2) On a certain day the highest temperature is 77 degrees and the lowest temperature is 61 degrees. What is the day's HDD?
A) 5
B) 12
C) 4
D) 0
Q3) Which of the following is a common use of weather derivatives?
A) Hedge the volume of electricity that will be demanded by customers in the summer
B) Hedge the price of oil that must be purchased in the winter
C) Hedge the price of electricity that must be purchased in the summer
D) Hedge the price and volume of gas that must be purchased for heating in the winter
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