Q&A Hero

Q: A stock has a historical volatility of 39%. The data shows significantly increased volatility in recent data and significantly lower volatility in older data. The implied estimate of the unconditional volatility using the GARCH model is most likely to be which of the following? A) 12% B) 25% C) 45% D) 85%

Q: Ask students to define Exotic options. Ask students to give examples of Exotic options. Have students define their example in terms of basic calls on puts. Demonstrate how all Exotic options are merely modified versions of basic options.

Q: What is the characteristic that makes options, like quantos, multivariate options?

Q: What purpose do currency linked options serve?

Q: How does a quanto hedge the currency risk a U.S. investor encounters when investing in foreign indexes?

Q: What is the risk a U.S. investor faces when investing in foreign index securities, besides index fluctuations?

Q: Donald Trump offers to give you a partnership share in his casinos if the price of his shares drops below a certain level. He charges a nominal fee for this right. What is he offering you and is he wise?

Q: A multivariate option that has a claim with a payoff determined by the average of two or more asset prices is known as:A) Basket optionsB) MultioptionsC) Quantos optionsD) Rainbow options

Q: A multivariate option that has a claim with a payoff dependent upon the price of two different assets is known as: A) Exotics B) Multioptions C) Quantos D) Supershares

Q: The concept created by Hakannson in 1976 to describe the exotic option like payoffs that could result without the need for a delta hedging requirement is known as: A) Exotics B) Multioptions C) Quantos D) Supershares

Q: The Nikkei index is 22,550, K = 21,000, σ = 0.19, rf = 0.04, S = 0.10, r = 0.08 and div = 0.01. The yen to dollar spot rate is 104 and the correlation coefficient is 0.30. What would be the dollar price of a 2-year equity-linked foreign exchange call? A) $45.02 B) $35.02 C) $25.01 D) $15.02

Q: The current Nikkei index price is 21,200. Assume σ = 0.13, r = 0.05 and div = 0.015. If K = 20,000 yen and yen per dollar spot rates are 103, what is the dollar value of a 2-year call? A) $13.97 B) $18.97 C) $23.97 D) $28.97

Q: Albert has accepted a wager to receive $5.00 if the price of Will Co. is above $35.00 per share. This right only exists if Will Co. drops below $33.00 sometime over the coming 100 days. Currently, Will Co. stock price is $38.24, r = 0.05, σ = 0.33, and div = 0. What is the value of Albert's position? A) $0.35 B) $0.25 C) $0.15 D) $0.05

Q: Cyril is purchasing a down-and-in cash call. H = $45.00, S = $38.24, K = $35, σ = 0.33, r = 0.05, div = 0 and it expires in 140 days. What is the value of the option if the payment is $1.00? A) $0.80 B) $1.80 C) $2.80 D) $3.80

Q: Suppose S = $52.50, K = $50, σ = 0.25, r = 0.04 and div = 0.01. What is the price of a gap option with 156 days until expiration and K1 = $32.00? A) $14.00 B) $15.00 C) $16.00 D) $17.00

Q: The Buckingham Casino offers to give every gambler one share of Buckingham Casino Corp. stock if the price drops below $40.00, as an incentive to spur business. If S = $45.25, σ = 0.15, r = 0.05 and div = 0, how much profit or loss is Buckingham incurring if they charge $0.25 to participate in this wager? A) $0.31 loss B) $0.31 profit C) $0.19 loss D) $0.19 profit

Q: The Buckingham Casino offers to give every gambler one share of Buckingham Casino Corp. stock if the price drops below $40.00, as an incentive to spur business. If S = $45.25, σ = 0.15, r = 0.05 and div = 0, how much is this offer worth if it expires in 30 days? A) $0.36 B) $0.26 C) $0.16 D) $0.06

Q: In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. Pat is paid one share of ABC Corp. stock if the price is below $85.00. What is the value of her wager? A) $21.80 B) $22.80 C) $23.80 D) $24.80

Q: Eugene holds a collect-on-delivery call with S = $36.50, K = $35, σ = 0.22, r = 0.04, div = 0 and 270 days until expiration. What is the value of the European COD call? A) $5.90 B) $6.90 C) $7.90 D) $8.90

Q: In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. If the price is below $85.00, Pat must pay $5.00. What is the net value of Pat's wager? A) -$2.49 B) +$2.49 C) -$1.50 D) +$1.50

Q: In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00. Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6 months. Pat receives nothing if the price is below $85.00. What is the value of her wager? A) $1.20 B) $2.20 C) $3.20 D) $4.20

Q: Randomly divide the class into two groups. Give one group the task of defending Warren Buffet's position on valuing put options. Have the other group disagree with Buffet's position. Moderate a discussion of the two, listing the pros and cons on the board.

Q: In the first-order condition for portfolio selection, explain the meaning of equilibrium.

Q: What does Girsanov's theorem tell us about drift and Brownian motion?

Q: How do probabilities change with a change of measure?

Q: How do asset values differ between using a traditional DCF approach and a stochastic discount factor approach?

Q: What aspect of risk-neutral pricing valuation links it to portfolio selection?

Q: In the case of a European Outperformance Option, we assume the strike asset is:A) CashB) A money market fundC) A stock or an indexD) A zero-coupon bond

Q: The case where the zero coupon bond is selected as the numeraire under a risky asset method results in a measure called the: A) Drift measure B) Forward measure C) Money market measure D) Spread measure

Q: Which of the following is not commonly used as a numeraire? A) Futures contract B) Money market account C) Risky asset D) Zero coupon bond

Q: The primary link between Brownian motion and Girsanov's theorem relates to which variable? A) Drift B) Numeraire C) Returns D) Standard deviation

Q: It can be said that Girsanov's theorem shows the equivalence of which two items? A) Change of drift and change of measure B) Change of numeraire and change of measure C) Change of drift and change of numeraire D) Change of numeraire and change of process

Q: When defining a change in measure, a redefining of the units in which a payoff is measured is called: A) Brownian motion B) Change of numeraire C) Stochastic discount factor D) Utility function

Q: The pricing of derivatives is linked to the decisions investors make relative to: A) Black-Scholes variables B) Money markets C) Portfolios D) T-bills

Q: In martingale pricing, the observed price of a stock follows a process which substitutes what variable for alpha? A) Delta B) Epsilon C) Money market rate D) Risk-free rate

Q: The risk-neutral measure arises when we select ________ as the numeraire. A) Asset portfolio B) Corporate bond C) Treasury bond D) Money market account

Q: The process of moving from one probability distribution to another is called: A) Brownian motion B) Change of measure C) Stochastic discount factor D) Utility function

Q: The ratio of the future uncertain martingale utility to the present known martingale utility is called: A) Brownian motion B) Change of measure C) Stochastic discount factor D) Utility function

Q: For a utility function that exhibits decreasing martingale utility, the martingale utility is low when: A) Consumption and utility are low B) Consumption and utility are high C) Consumption is low and utility is high D) Consumption is high and utility is low

Q: For a utility function that exhibits decreasing martingale utility, the martingale utility is high when: A) Consumption and utility are low B) Consumption and utility are high C) Consumption is low and utility is high D) Consumption is high and utility is low

Q: How does the Black-Scholes equation explain the pricing of derivatives?

Q: Give an example of currency translation that is a change in numeraire.

Q: Define a power option.

Q: Briefly define a terminal boundary condition.

Q: How does a dividend payment impact the option price?

Q: Explain the relationship between strike prices and implied volatilities under a price jump scenario.

Q: Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. At approximately what stock price will the wager be of equal value to both Joe and Sarah?A) $32.00B) $33.30C) $34.25D) $35.00

Q: Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. If Sarah agrees to the bet, what is the value of her wager? A) $3.00 B) $9.65 C) $12.44 D) $19.58

Q: Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6 months (180 days). The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. What is the value of the wager to Joe? A) $3.00 B) $9.65 C) $12.44 D) $19.58

Q: Assume S = $48.35, K = 45, σ = 0.23, r = 0.04, T - t = 60 days, div = 0, and a jump probability = 0.005. What is the increase in the value of a call over a no-jump call? A) $0.04 B) $0.03 C) $0.02 D) $0.01

Q: Assume S = $52.50, K = $55, σ = 0.20, r = 0.045, T - t = 130 days, div = 0.01, and a jump probability = 0.007. What is the value of a put option? A) $3.63 B) $2.63 C) $1.63 D) $0.63

Q: Assume S = $60, K = $65, σ = 0.15, r = 0.05, T - t = 122 days, div = 0.015, and a jump probability = 0.003. What is the value of a call? A) $0.67 B) $1.67 C) $2.67 D) $3.67

Q: Mary wagers to pay one share of stock to Matt if the price at expiration in 1 year is above $75.00. Assume S(0) = 60.00, σ = 0.15, r = 0.04, and dividend rate = 0.01. What is the value of Mary's bet? A) $6.55 B) $7.55 C) $8.55 D) $9.55

Q: Which of the following examples does not involve different numeraire? A) Currency translation B) Quantity uncertain C) Backward equation D) All-or-nothing options

Q: Which of the following equations represents a call power option? A) Min (Ka-Sa,0) B) Max (Ka-Sa,0) C) Min (Sa-Ka,0) D) Max (Sa-Ka,0)

Q: What do we call an option in which the holder has a claim that pays one share of stock if S(T) > K, and nothing otherwise? A) Cash-or-nothing option B) Asset-or-nothing option C) Exotic option D) Digital cash

Q: What is the boundary condition for a European put option? A) Max [0,S(T)-K] B) Max [0,K-S(T)] C) Min [0,S(T)-K] D) Min [0,K-S(T)]

Q: What is the boundary condition for a European call option? A) Max [0,S(T)-K] B) Max [0,K-S(T)] C) Min [0,S(T)-K] D) Min [0,K-S(T)]

Q: What term is sometimes used to describe the price at a particular point in time, say maturity, that is necessary to calculate today's price? A) Face value B) Par value C) Boundary condition D) All of the above

Q: Why is Brownian motion the foundation for modern derivatives pricing models?

Q: What is the relationship of the Sharpe ratios and risk premiums between stocks and options?

Q: When considering drift and noise, how would you explain price movements over smaller and smaller time intervals?

Q: Define the term drift.

Q: Provide a definition of Brownian motion.

Q: What are two important implications of assuming that prices follow a geometric Brownian motion?

Q: The deterministic drift of a pure Brownian motion that is virtually undetectable is sometimes referred to as the:A) DistributionB) Expected returnC) Random walkD) Standard deviation

Q: A Brownian motion is a stochastic process that can be described as a: A) Pattern of movements with continuous movements B) Pattern of movements with discrete movements C) Random walk with continuous movements D) Random walk with discrete movements

Q: For purposes of option pricing, when the movement of a stock price follows a geometric Brownian motion, the stock price is said to follow which type of distribution? A) Bimodal B) Latin hypercube C) Lognormal D) Normal

Q: A modification to the Brownian process in which the drift and volatility depend on the stock price is called: A) Ornstein-Uhlenbeck B) Diffusion C) Ito D) Geometric

Q: A modification to the Brownian process that permits mean reversion is called:A) Ornstein-UhlenbeckB) DiffusionC) ItoD) Geometric

Q: The value of Z(t) at any point in time can be described as a process in which there is a cumulative effect of infinitely small movements. This process is called: A) Ornstein-Uhlenbeck B) Diffusion C) Ito D) Geometric

Q: Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.20, S(0) = 45, S(Q) = 55, r = 0.03, σs = 0.18 σQ = 0.28, and no dividends. Using formula 20.39, what is the price of a claim that pays 1/? A) $3.02 B) $2.02 C) $1.02 D) $0.02

Q: Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.65, S(0) = 55, Q(0) = 60, r = 0.04, σs = 0.22 σQ = 0.15, and dividends = 0. Using formula 20.39, what is the price of a claim that pays Q/? A) $8.16 B) $9.16 C) $10.16 D) $11.16

Q: Assume the following: LN(S) and LN(Q) have a correlation coefficient of 0.40, S(0) = 60, Q(0) = 60, r = 0.05, σs = 0.30 σQ = 0.25, and dividend = 0. Using formula 20.39, what is the price of a claim that pays ? A) $243.96 B) $322.96 C) $479.96 D) $532.96

Q: Assume a stock price of S(0) = $80.00, r = 0.05, σ = 0.35, and dividend = 0.01. What is the price of a claim that pays S-2/3? Use formula 20.29. A) $0.25 B) $0.35 C) $0.05 D) $0.15

Q: Assume a stock price of S(0) = $45.00, r = 0.03, σ = 0.40, and dividend = 0.015. What is the price of a claim that pays ? Use formula 20.29. A) $6.41 B) $5.41 C) $4.41 D) $3.41

Q: Assume a stock price of S(0) = $83.00, r = 0.045, σ = 0.25, and dividend = 0.02. What is the price of a claim that pays S3? Use formula 20.29. A) $423,323 B) $710,695 C) $624,165 D) $818,123

Q: Assume a stock price of S(0) = $62.00, r = 0.05, σ = 0.30, and dividend = 0. What is the price of a claim that pays ? Use formula 20.29. A) $7.59 B) $8.59 C) $9.59 D) $10.59

Q: Ask the class to state how simulations could be used to improve pricing models. Highlight situations where historical results violated pricing assumptions and how simulations may have provided better results.

Q: What advantage does a variance reduction technique offer?