Quantitative Finance Study Guide
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Course Introduction
Quantitative Finance explores the application of mathematical models, statistical techniques, and computational methods to analyze financial markets and securities. This course covers topics such as derivative pricing, risk management, portfolio optimization, and financial econometrics, emphasizing the use of quantitative tools to solve complex problems in investment and financial decision-making. Students will learn to implement models using programming languages, interpret quantitative results, and understand the practical implications of quantitative finance in areas including trading, asset management, and financial engineering.
Recommended Textbook Fundamentals of Futures and Options Markets 9th 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 February 1 is $48. A trader sells 200 put options on the stock with a strike price of $40 when the option price is $2. The options are exercised when the stock price is $39. The trader's net profit or loss is
A) Loss of $800
B) Loss of $200
C) Gain of $200
D) Loss of $900
Answer: C
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Chapter 2: Futures Markets and Central Counterparties
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Q1) Clearing houses are
A) Never used in futures markets and sometimes used in OTC markets
B) Used in OTC markets, but not in futures markets
C) Sometimes used in both futures markets and OTC markets
D) Always used in both futures markets and OTC markets
Answer: C
Q2) Which of the following is NOT true
A) Futures contracts nearly always last longer than forward contracts
B) Futures contracts are standardized; forward contracts are not.
C) Delivery or final cash settlement usually takes place with forward contracts; the same is not true of futures contracts.
D) Forward contracts usually have one specified delivery date; futures contract often have a range of delivery dates.
Answer: A
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4
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 is necessary for tailing a hedge?
A) Comparing the size in units of the position being hedged with the size in units of the futures contract
B) Comparing the value of the position being hedged with the value of one futures contract
C) Comparing the futures price of the asset being hedged to its forward price
D) None of the above
Answer: B
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Chapter 4: Interest Rates
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Q1) Prior to the credit crisis that started in 2007 which of the following was the proxy used by derivatives traders for the risk-free rate
A) The Treasury rate
B) The LIBOR rate
C) The repo rate
D) The overnight indexed swap rate
Q2) Which of following describes forward rates?
A) Interest rates implied by current zero rates for future periods of time
B) Interest rate earned on an investment that starts today and last for n-years in the future without coupons
C) The coupon rate that causes a bond price to equal its par (or principal) value
D) A single discount rate that gives the value of a bond equal to its market price when applied to all cash flows
Q3) At what interest rate does a government borrow in its own currency?
A) Treasury rate
B) LIBOR
C) LIBID
D) Repo rate
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6
Chapter 5: Determination of Forward and Futures Prices
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Q1) Which of the following is NOT true?
A) Gold and silver are investment assets
B) Investment assets are held by significant numbers of investors for investment purposes
C) Investment assets are never held for consumption
D) The forward price of an investment asset can be obtained from the spot price, interest rates and the income paid on the asset
Q2) Which of the following describes a known dividend yield on a stock?
A) The size of the dividend payments each year is known
B) Dividends per year as a percentage of today's stock price are known
C) Dividends per year as a percentage of the stock price at the time when dividends are paid are known
D) Dividends will yield a certain return to a person buying the stock today
Q3) Which of the following is NOT a reason why a short position in a stock is closed out?
A) The investor with the short position chooses to close out the position
B) The lender of the shares issues instructions to close out the position
C) The broker is no longer able to borrow shares from other clients
D) The investor does not maintain margins required on his/her margin account
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Chapter 6: Interest Rate Futures
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Q1) Which of the following is true?
A) The futures rates calculated from a Eurodollar futures quote are always less than the corresponding forward rate
B) The futures rates calculated from a Eurodollar futures quote are always greater than the corresponding forward rate
C) The futures rates calculated from a Eurodollar futures quote should equal the corresponding forward rate
D) The futures rates calculated from a Eurodollar futures quote are sometimes greater than and sometimes less than the corresponding forward rate
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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Chapter 7: Swaps
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Q1) Which of the following is a typical bid-offer spread on the swap rate for a plain vanilla interest rate swap?
A) 3 basis points
B) 8 basis points
C) 13 basis points
D) 18 basis points
Q2) Which of the following describes an interest rate swap?
A) A way of converting a liability from fixed to floating
B) A portfolio of forward rate agreements
C) An agreement to exchange interest at a fixed rate for interest at a floating rate
D) All of the above
Q3) A company enters into an interest rate swap where it is paying fixed and receiving LIBOR. When interest rates increase, which of the following is true?
A) The value of the swap to the company increases
B) The value of the swap to the company decreases
C) The value of the swap can either increase or decrease
D) The value of the swap does not change providing the swap rate remains the same
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. (The portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created from the mezzanine tranches with the same allocation of principal. Losses on the mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are losses on the mezzanine tranche of the ABS
A) 50%
B) 60%
C) 80%
D) 100%
Q2) Which of the following describes the S&P/Case-Shiller index?
A) A stock market index
B) An index of interest rates on mortgages
C) An index of house prices
D) An index showing the dollar amount of mortgages granted each month
Q3) Which of the following is true of a non-recourse mortgage?
A) The house buyer, if unable to make payments, can lose all possessions
B) The house buyer has an American style put option on the house
C) The house buyer has a European style put option on the house
D) The lender is less likely to lose money on the mortgage
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Chapter 9: Mechanics of Options Markets
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Q1) An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash dividend. Which of the following is then the position of the investor?
A) The investor has put options to sell 100 shares for $20
B) The investor has put options to sell 100 shares for $19
C) The investor has put options to sell 105 shares for $19
D) The investor has put options to sell 105 shares for $19.05
Q2) 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
Q3) Which of the following are true for CBOE stock options?
A) There are no margin requirements
B) The initial margin and maintenance margin are determined by formulas and are equal
C) The initial margin and maintenance margin are determined by formulas and are different
D) The maintenance margin is usually about 75% of the initial margin
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Chapter 10: Properties of Stock Options
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Q1) When the stock 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
Q2) Which of the following can be used to create a long position in a European put option on a stock?
A) Buy a call option on the stock and buy the stock
B) Buy a call on the stock and short the stock
C) Sell a call option on the stock and buy the stock
D) Sell a call option on the stock and sell the stock
Q3) Which of the following is NOT true?
A) An American put option is always worth less than the present value of the strike price
B) A European put option is always worth less than the present value of the strike price
C) A European call option is always worth less than the stock price
D) An American call option is always worth less than the stock price
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Chapter 11: Trading Strategies Involving Options
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Q1) Which of the following creates a bear spread?
A) Buy a low strike price call and sell a high strike price call
B) Buy a high strike price call and sell a low strike price call
C) Buy a low strike price call and sell a high strike price put
D) Buy a low strike price put and sell a high strike price call
Q2) Which of the following is correct?
A) A diagonal spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different
B) A diagonal spread can be created by buying a put and selling a call when the strike prices are the same and the times to maturity are different
C) A diagonal spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different
D) A diagonal spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different
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13
Chapter 12: Introduction to Binomial Trees
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Q1) A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%.
A) The parameters p and u are the same for both trees
B) The parameter p is the same for both trees but u is not
C) The parameter u is the same for both trees but p is not
D) None of the above
Q2) In a binomial tree created to value an option on a stock, what is the expected return on the option?
A) Zero
B) The return required by the market
C) The risk-free rate
D) It is impossible to know without more information
Q3) In a binomial tree created to value an option on a stock, the expected return on stock is
A) Zero
B) The return required by the market
C) The risk-free rate
D) It is impossible to know without more information
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Chapter 13: Valuing Stock Options: the Bsm Model
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Q1) When there are two dividends on a stock, Black's approximation sets the value of an American call option equal to which of the following
A) The value of a European option maturing just before the first dividend
B) The value of a European option maturing just before the second (final) dividend
C) The greater of the values in A and B
D) The greater of the value in B and the value assuming no early exercise
Q2) The volatility of a stock is 18% per year. What is the volatility per month?
A) 1.5%
B) 3.0%
C) 5.2%
D) None of the above
Q3) Which of the following is a way of extending the Black-Scholes-Merton formula to value a European call option on a stock paying a single dividend?
A) Reduce the maturity of the option so that it equals the time of the dividend
B) Subtract the dividend from the stock price
C) Add the dividend to the stock price
D) Subtract the present value of the dividend from the stock price
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Page 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 ensures that managers are rewarded only when a company performs better than its competitors?
A) A constant strike price for executive stock options
B) A strike price that increases with time
C) A strike price that changes in line with an index of stock prices
D) A strike price that is tied to reported profit
Q3) Which of the following increases the expected life of employee stock options?
A) An increase in the vesting period
B) An increase in employee turnover
C) A fast growth rate for the stock price
D) A tendency for employees to exercise earlier than in the past
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Page 16
Chapter 15: Options on Stock Indices and Currencies
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Q1) Which of the following describes what a company should do to create a range forward contract in order to hedge foreign currency that will be received?
A) Buy a put and sell a call on the currency with the strike price of the put higher than that of the call
B) Buy a put and sell a call on the currency with the strike price of the put lower than that of the call
C) Buy a call and sell a put on the currency with the strike price of the put higher than that of the call
D) Buy a call and sell a put on the currency with the strike price of the put lower than that of the call
Q2) A binomial tree with one-month time steps is used to value an index option. The interest rate is 3% per annum and the dividend yield is 1% per annum. The volatility of the index is 16%. What is the probability of an up movement?
A) 0.4704
B) 0.5065
C) 0.5592
D) 0.5833
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Page 17
Chapter 16: Futures Options and Blacks Model
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Q1) Which of the following is acquired (in addition to a cash payoff) when the holder of a call futures exercises?
A) A long position in a futures contract
B) A short position in a futures contract
C) A long position in the underlying asset
D) A short position in the underlying asset
Q2) Which of the following is true?
A) A futures option is settled daily
B) A futures-style option is settled daily
C) Both a futures option and a futures-style option are settled daily
D) Neither a futures option nor a futures-style option is settled daily
Q3) Which of the following is true when the futures price exceeds the spot price?
A) Calls on futures should never be exercised early
B) Put on futures should never be exercised early
C) A call on futures is always worth at least as much as the corresponding call on spot
D) A call on spot is always worth at least as much as the corresponding call on futures
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Chapter 17: The Greek Letters
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Q1) Maintaining a delta-neutral portfolio is an example of which of the following
A) Stop-loss strategy
B) Dynamic hedging
C) Hedge and forget strategy
D) Static hedging
Q2) 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
Q3) Which of the following could NOT be a delta-neutral portfolio?
A) A long position in call options plus a short position in the underlying stock
B) A short position in call options plus a short position in the underlying stock
C) A long position in put options and a long position in the underlying stock
D) A long position in a put option and a long position in a call option
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19
Chapter 18: Binomial Trees in Practice
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Q1) The values of a stock price at the end of the second time step are $80, $100, $125. The corresponding values of an option are $0, $5, and $20 respectively. What is an estimate of gamma?
A) 0.136
B) 0.146
C) 0.156
D) 0.166
Q2) When the stock price is 20 and the present value of dividends is 2, which of the following is the recommended way of constructing a tree?
A) Draw a tree for an initial stock price of 20 and subtract the present value of future dividends at each node
B) Draw a tree for an initial stock price of 22 and subtract the present value of future dividends at each node
C) Draw a tree with an initial stock price of 18 and add the present value of future dividends at each node
D) Draw a tree with an initial stock price of 18 and add 2 at each node
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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) Which of the following is true?
A) The volatility skew for equities is much more pronounced now than it was in 1985.
B) The volatility skew for equities has a positive gradient
C) The volatility skew for equities is consistent with the Black-Scholes-Merton model.
D) The volatility skew for equities is similar to that for foreign currencies.
Q3) Which of the following could cause the volatility smile typically seen for foreign currency options?
A) Currencies are traded in different countries at different times of the day
B) Currencies tend to have low volatilities
C) The activities of central banks causes occasional jumps in the exchange rate
D) Interest rates may be different in the two countries
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Chapter 20: Value at Risk and Expected Shortfall
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Q1) What is the method of testing how often a VaR with a certain confidence level was exceeded in the past called?
A) Stress testing
B) Backtesting
C) EWMA
D) The model-building approach
Q2) Which of the following is true?
A) Cash flow mapping is a way of calculating the present value of cash flows
B) Cash flow mapping is used to handle interest rate exposures in the model building approach
C) Cash flow mapping is used to handle interest rate exposures in the historical simulation approach
D) None of the above
Q3) The gain from a project is equally likely to have any value between -$0.15 million and +$0.85 million. What is the 99% expected shortfall?
A) $0.145 million
B) $0.14 million
C) $0.13 million
D) $0.10 million
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Page 22
Chapter 21: Interest Rate Options
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Q1) In put-call parity for caps and floors, which of the following is true?
A) Long cap plus long floor equals swap
B) Long cap plus swap equals short floor
C) Long cap equals long floor plus swap
D) Long cap minus long floor equals swaption
Q2) Which of the following is assumed to be lognormal when a bond option is valued?
A) A future bond price
B) A future swap rate
C) A future short-term rate
D) A future bond yield
Q3) Which of the following is assumed to be lognormal when a caplet is valued?
A) A future bond price
B) A future swap rate
C) A future short-term rate
D) A future long-term rate
Q4) Which of the following is true?
A) A callable bond allows the lender to ask for the principal to be repaid early
B) A callable bond allows the borrower to repay the principal early
C) A callable bond is a bond with an embedded stock option
D) None of the above
23
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Chapter 22: Exotic Options and Other Nonstandard Products
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Q1) There are two types of regular options (calls and puts). How many types of compound options are there?
A) Two
B) Four
C) Six
D) Eight
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
Q3) Which of the following are subject to prepayment risk?
A) Collateralized mortgage obligations
B) POs
C) IOs
D) All of the above
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Page 24
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) Which of the following is true about a CDS?
A) Restructuring is never a credit event
B) Restructuring is always a credit event
C) Certain types of restructuring qualify as credit events but others do not
D) Sometimes a CDS is defined so that restructuring is a credit event and sometimes it is not
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Chapter 24: Weather, Energy, and Insurance Derivatives
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Q1) Which of the following is the basis for calculating HDD and CDD?
A) The average temperature during the day
B) The average of the highest and lowest temperature during the day
C) The temperature at 12 noon during the day
D) None of the above
Q2) Which of the following describes the period during which a "5 times 16" contract provides electricity?
A) From 7am to 11pm on five successive days
B) From 4pm to 8am on five successive days
C) For any 5 hours of a day on 16 successive days
D) For any 16 hours of a day in five successive days
Q3) Which of the following is NOT true about electricity?
A) Supply and demand for electricity are matched within 140 control areas in the US, then excess power sold to other control areas
B) The ability to sell excess power is constrained by transmission capacity
C) Electricity is a commodity that can be easily stored
D) Air conditioning is a big use of electricity
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