7. Derivatives

Question: At the inception of a market-rate plain vanilla swap, the value of the swap to the fixed-rate payer is:

• A) positive
• B) zero
• C) either positive or negative. Chantal DuPont is the CFO of Vetements Verdun, a manufacturer of specialty clothing and uniforms, located in northern France. The firm is currently undergoing an expansion which will require DuPont to draw down 25 million on Vetements Verdun's credit line as a 90-day bridge loan before the mortgage closes. The money will not be needed for 60 days, at which point the interest rate will be determined. The interest rate on the loan will be based off 90- day LIBOR. DuPont is becoming concerned because of signs that interest rates may begin to rise. The firm cannot afford to have its borrowing costs increase significantly over current rates. In response to DuPont's concerns, the company's CEO, Viviane Lamarre, has asked DuPont to hedge the firm's borrowing costs, even if that entails some near-term outlays. DuPont and Lamarre discuss entering into a forward rate agreement (FRA) to hedge Vetements Verdun's interest rate exposure on the credit line. Current LIBOR rates are: LIBOR rate 30-day 2.6% 60-day 2.8% 90-day 3.0% 120-day 3.2% 150-day 3.3% 180-day 3.4% They decide to go forward with the hedge and DuPont enters into the appropriate FRA for the full amount of 25 million

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Question: Which statement most accurately describes a 2 x 3 forward rate agreement?

• A) Contract expires in two months on an underlying loan settled in three months Correct
• B) Two-month underlying interest rate on a contract settled in three months
• C) Underlying loan of two month maturity under a contract that expires in three months

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Question: Which forward rate agreement would most effectively hedge Vetements Verdun's exposure to LIBOR?

• A) 3 x 2
• B) 2 x 5
• C) 2 x 3

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Question: Which value is closest to the price of the most effective hedge for Vetements Verdun?

• A) 3.3%
• B) 3.6%
• C) 3.0%

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Question: What must the 90-day LIBOR rate have been at the expiration of the contract?

• A) 3.6%
• B) 4.0%
• C) 3.4%

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Question: The current U.S. dollar ($) to Canadian dollar (C$) exchange rate is 0.7. In a $1 million currency swap, the party that is entering the swap to hedge existing exposure to C$- denominated fixed-rate liability will:

• A) pay C$1,428,571 at the beginning of the swap
• B) pay floating in C$
• C) receive floating in C$

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Question: Calculate the price (expressed as an annualized rate) of a 1x4 forward rate agreement (FR

• A) 7.47%
• B) 6.86%
• C)

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Question: Consider a one-year currency swap with semiannual payments. The payments are in U.S. dollars and euros. The current exchange rate of the euro is $1.30 and interest rates are 180 days 360 days USD MRR 5.6% 6.0% MRR 4.8% 5.4% What is the fixed rate in euros?

• A) 5.318%
• B) 2.659%
• C) 5.245%

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Question: The contract price of a forward contract is:

• A) always the present value of the expected future spot price Correct
• B) determined at the settlement date
• C) the price that makes the contract a zero-value investment at initiation

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Question: Writing a series of interest-rate puts and buying a series of interest-rate calls, all at the same exercise rate, is equivalent to:

• A) being the floating-rate payer in an interest rate swap
• B) being the fixed-rate payer in an interest rate swap Correct
• C)

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Question: The no-arbitrage price of a futures contract with a spot rate of 990, a time to maturity of 2 years, and a risk-free-rate of 5% is closest to:

• A) 1091
• B) 1040
• C) 792

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Question: The fixed-rate on a semiannual 2-year interest rate swap is closest to the:

• A) coupon rate on a 2-year par bond with the same credit risk as the reference rate
• B) coupon rate on a 2-year par bond with the same credit risk as the fixed-rate payer
• C) current 180-day T-bill rate. The Isle of Nefer is a developing country with its stock and futures markets enjoying record trading volumes due to the influx of foreign funds. You are looking to invest in the stock and futures markets in the Isle of Nefer. The representative stock market index, Nefer Industrial Index (NII), is currently priced at 8,765 and the one year NII future contract is currently trading at 8,920. You have experience in using forward contracts but not futures. You discuss the possibility of investing in the Isle of Nefer using futures contract with your supervisor, Peter Filler, and he makes the following comments. Comment 1: "A futures contract will have positive value after marking to market if the future price is up on that day." Comment 2: "Given a quoted clean bond price of the CTD, when looking at a bond future the full price of the bond must be used which equals the clean price of the bond plus accrued interest. The futures price can then be calculated as:

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Question: How will the price of the one-year stock index future perform over the next 12 months?

• A) The futures price will converge to the future spot index price, with the basis reducing to zero
• B) The value will move approximately in line with the spot index price, with a fairly constant basis
• C) The futures price will move approximately in line with the spot index price, though its actual level at the end of the year will depend more on supply and demand than on the spot price

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Question: Comment 1 is best described as:

• A) correct
• B)
• C)

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Question: Comment 2 is best described as:

• A) correct
• B) incorrect as the full price should be the clean price less the current accrued interest
• C) incorrect as the accrued interest at expiration should be deducted from the future value of full bond price in arriving at the quoted futures price

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Question: Using Exhibit 1, the quoted price of the Treasury bond futures contract should be closest to:

• A) $941
• B) $975
• C) $1,100

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Question: To initiate an arbitrage trade if the futures contract is underpriced, the trader should:

• A) borrow at the risk-free rate, short the asset, and sell the futures
• B) short the asset, invest at the risk-free rate, and buy the futures Correct
• C) borrow at the risk-free rate, buy the asset, and sell the futures

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Question: days ago, J. Klein took a short position in a $10 million (3X6) forward rate agreement (FR

• A) −$15,154
• B) −$15,495
• C) −$15,280

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Question: The fixed-rate payer in an interest-rate swap has a position equivalent to a series of:

• A) long interest-puts and short interest-rate calls
• B) long interest-rate puts and calls Correct
• C) short interest-rate puts and long interest-rate calls. Craig Champion, CFA, manages portfolios of U.S. securities for European investors. His clients have each hold different kinds of securities, and each has differing views with respect to hedging exchange rate risk

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Question: Champion and Silvers each gave a reason for why the futures price of the S&P 500 index might be less than the spot price. With respect to their statements, it is most accurate to conclude that:

• A) neither statement is valid
• B) Champion's statement is invalid while Silver's statement is valid Correct
• C)

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Question: For a futures contract on an asset with no storage costs, convenience yield, or other expected cash flows over the term of the contract, there should be a:

• A) positive correlation between the futures price and interest rates and a negative correlation between the futures price and the spot price
• B) negative correlation between the futures price and interest rates and a positive correlation between the futures price and the spot price
• C) positive correlation between the futures price and both interest rates and the spot price

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Question: Oil futures prices might be higher than the spot price because:

• A) of reverse contango
• B) there are more costs than benefits to holding the asset Correct
• C) there are more benefits than costs to holding the asset

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Question: The no-arbitrage futures price of the Euro-bond contract is closest to:

• A) €94.83
• B) €102.85
• C) €110.61

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Question: A plain vanilla interest-rate swap to the fixed-rate payer is equivalent to issuing a fixed-rate bond and:

• A) buying a floating-rate bond Correct
• B) selling a series of interest rate calls
• C) selling a series of interest rate puts

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Question: Consider a fixed-for-fixed 1-year $100,000 semiannual currency swap with rates of 5.0% in USD and 4.8% in CHF, originated when the exchange rate is $0.34. After the first settlement, the exchange rate is $0.35 and the term structure is: 90 days 180 days MRR 5.2% 5.6% Swiss 4.8% 5.4% What is the value of the swap to the USD payer?

• A) $2,814
• B) $2,937
• C) -$2,719

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Question: For a 1-year quarterly-pay swap, an equivalent position with short puts and long calls would involve:

• A) three put-call combinations expiring on the first three settlement dates of the swap
• B) put-call combinations expiring on each of the four settlement dates Correct
• C) three put-call combinations on the last three settlement dates of the swap

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Question: The price and value of a plain vanilla interest-rate swap are:

• A) never equal
• B) only equal at the inception of a swap contract Correct
• C) equal in equilibrium

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Question: Consider a fixed-rate semiannual-pay equity swap where the equity payments are the total return on a $1 million portfolio and the following information: 180-day MRR is 5.2% 360-day MRR is 5.5% Dividend yield on the portfolio = 1.2% What is the fixed rate on the swap?

• A) 5.4197%
• B) 5.1387%
• C) 5.4234%

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Question: At expiration, the value of a forward contract is:

• A) always greater than or equal to zero
• B) the difference between the contract price and the market value of the underlying asset
• C) equal to the market price of the underlying asset

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Question: Which of the following comments relating to Brodeur's use of a forward rate agreement is least accurate?

• A) A short FRA can be used to lock into a fixed rate of borrowing commencing in two months’ time and expiring in five months’ time
• B) The use of a FRA to hedge interest rate risk would lock Brodeur into paying a fixed rate plus 40 basis points for her borrowing
• C) The use of a FRA to hedge interest rate risk on her future loan will mean that she no longer benefits if interest rates fall

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Question: Using the data in Exhibit 1, which of the following is closest to the forward price of the FRA?

• A) 2.4%
• B) 2.8%
• C) 3.0%

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Question: For this question only, assume that the forward price of the FRA was 2.9%. Which of the following is the closest to the value accrued on the FRA from Brodeur's perspective one month after initiation of the contract?

• A) +€2,300
• B) +€2,200
• C) –€2,265

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Question: In an equity return swap for MRR, if the return on the underlying equity portfolio is negative for a payment period, the equity return payer will:

• A) receive a net payment greater than the loss of value on the equity portfolio Correct
• B) make a net payment greater than the loss of value on the equity portfolio
• C) receive a net payment less than the loss of value on the equity portfolio

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Question: A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:

• A) $110.00
• B) $110.06
• C) $110.20

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Question: Consider a 9-month forward contract on a 10-year 7% Treasury note just issued at par. The effective annual risk-free rate is 5% over the near term and the first coupon is to be paid in 182 days. The price of the forward is closest to:

• A) 965.84
• B) 1,037.27
• C)

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Question: Consider a 1-year, $5 million semiannual-pay fixed-rate equity swap initiated when the equity index is 750 and swap fixed rate is 3.7%. Equity index was at 760 at first settlement. It is now 270 days since inception of the swap and the index is at 767, 90-day MRR is 3.4% (DF = 0.99157) and 270-day MRR is 3.7% (DF = 0.9730). What is the value of the swap to the fixed- rate payer?

• A) $3,478
• B) −$2,726
• C) −$3,520

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Question: The value of the S&P 500 Index is 1,260. The continuously compounded risk-free rate is 5.4% and the continuous dividend yield is 3.5%. Calculate the no-arbitrage price of a 160-day forward contract on the index.

• A) $562.91
• B) $1,270.54
• C) $1,310.13

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Question: The theoretical price of a forward contract:

• A) equals the long’s expectation of the future price of the underlying asset Correct
• B) is the no-arbitrage price
• C) is always greater than the current price of the underlying asset

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Question: A U.S. firm (U.S.) and a foreign firm (F) engage in a 3-year, annual pay currency swap; The USD fixed rate at initiation was 5% while FC fixed rate was 4%. At the beginning of the swap, $2 million was paid by the U.S. firm and the exchange rate was 2 FC units per $1. At the end of the swap period the exchange rate was 1.75 FC units per $1. At the end of year 1, firm:

• A) U.S. pays firm F 160,000 FC units Correct
• B) F pays firm U.S. $200,000
• C) U.S. pays firm F $200,000

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Question: Calculate the price of a 200-day forward contract on an 8%, semi-annual, U.S. Treasury bond with a spot price of $1,310. Next coupon payment will be made in 150 days. The annual risk- free rate is 5%.

• A) $1,333.50
• B) $1,270.79
• C) $1,305.22

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Question: The price of a forward contract:

• A) depends on forward interest rates Correct
• B) is determined at contract initiation
• C) changes over the term of the contract

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Question: Which of the following is equivalent to a plain vanilla receive-fixed interest rate swap?

• A) A short position in a bond coupled with the issuance of a floating rate note
• B) A short position in a bond coupled with a long position in a floating rate note Correct
• C) A long position in a bond coupled with the issuance of a floating rate note

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Question: Over the life of a swap, the price of the swap:

• A) is approximately equal to the market value of the swap
• B) fluctuates with changes in the yield curve
• C) does not change

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Question: The fixed-rate receiver in a plain vanilla interest rate swap has a position equivalent to a series of:

• A) short interest-puts and long interest-rate calls Correct
• B) long interest-rate puts and short interest-rate calls
• C) long interest-rate puts

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Question: Consider a 1-year semiannual equity swap based on an index at 985 and a fixed rate of 4.4%. 90 days after the initiation of the swap, the index is at 982 and MRR is 4.6% for 90 days and 4.8% for 270 days. The value of the swap to the equity payer, based on a $2 million notional value is closest to:

• A) −$22,564
• B) $22,314
• C) $22,564

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Question: At contract initiation, the value of a forward contract:

• A) is typically zero regardless of the price of the underlying asset Correct
• B) is set to 100 by convention
• C) depends on the market price of the underlying asset

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Question: The price of a forward contract:

• A) is equal to the value of the contract in equilibrium
• B) is the settlement price for the underlying asset Correct
• C) must be equal to the market price at contract termination. Abel Smith works in the Treasury Department of OTS Ltd. OTS is an international construction firm, based in the United States. OTS hopes to raise €100 million through the issuance of a €100 million one-year fixed rate bond but is concerned about the currency risk exposure. TNA Bank proposed a one year EUR-USD currency swap with semi-annual settlements to OTS to mitigate the exchange rate risk. The notional principal would be €100 million. The

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Question: Has the bank correctly calculated the fixed rates on the currency swap?

• A) Both fixed rates are incorrectly calculated Correct
• B) One of the two fixed rates is incorrectly calculated
• C) Both fixed rates are correctly calculated

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Question: Using the information in Exhibit 2, what is the market value of the equity swap to OTS three months after swap initiation?

• A) +USD80.35 million Correct
• B) +USD85.33 million
• C) +USD88.76 million

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Question: How many of Smith's comments are correct?

• A) Neither comment is correct
• B) One comment is correct
• C) Both comments are correct

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Question: The price of an interest rate swap is the:

• A) cost to purchase a swap
• B) fixed rate of interest Correct
• C) market value of the swap

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Question: In which type of swap contract is notional principal most likely to be exchanged at initiation?

• A) Currency swap Correct
• B) Equity swap
• C) Interest rate swap

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Question: An equity portfolio manager who has a positive long-term outlook for equities, but expects equity prices to decline over the next three months, would most appropriately enter into:

• A) a short straddle with an equity index as the underlying
• B) an equity swap as the equity return receiver Correct
• C) an equity swap as the equity return payer

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Question: What is the difference between spot and futures prices? Spot prices are always:

• A) delivered to meet the futures obligation at expiration
• B) equal to the futures price at futures expiration Correct
• C) lower than futures prices

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Question: During the life of a forward contract, the value of the contract is best described as:

• A) the difference between the spot price and the present value of the forward price of the underlying asset
• B) the difference between the future value of the spot price and the expected future price of the underlying asset
• C) the present value of the expected future price of the underlying asset

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Question: The floating-rate payer in a simple interest-rate swap has a position that is equivalent to:

• A) a series of long forward rate agreements (FRAs)
• B) a series of short FRAs
• C) issuing a floating-rate bond and a series of long FRAs.

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Question: Consider a fixed-rate semiannual-pay equity swap where the equity payments are the total return on a $1 million portfolio and the following information: 180-day MRR is 4.2% 360-day MRR is 4.5% Div. yield on the portfolio = 1.2% What is the fixed rate on the swap?

• A) 4.3232%
• B) 4.5143%
• C) 4.4477%

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Question: A company has chosen to use a 6 x 9 FRA expiring in 6 months to mitigate the risk of paying a floating coupon on the bond issue. The current term structure for MRR is as follows: Term Interest Rate 180 days 5.65% 270 days 5.95% What is the price of this forward rate agreement (FRA)?

• A) 3.19%
• B) 6.37%
• C) $6.37

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Question: The price of a 3 × 5 forward rate agreement (FR

• A) 2-month implied forward rate 3 months from today Correct
• B) 3-month implied forward rate 5 months from today
• C) 2-month implied forward rate 5 months from today

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Question: A swap is equivalent to a series of:

• A) FRAs priced at market rates Correct
• B) off-market FRAs
• C) interest rate calls. John Williams, CFA, works in the treasury department of Sam Smith Leisure Inc., a U.S. based manufacturer of gym equipment. Recently he has been considering using derivative instruments to lock in returns on excess cash flows that tend to accumulate in the final quarter of each year as demand for equipment peaks during that time. He estimates that this year, in 60-days, the company will have $28.5 million in excess funds to invest for 90 days. Williams is presenting to the board 60 days before the excess funds need to be deposited, which is also 30 days before the year end. He intends to suggest an FRA as a method of

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Question: Which of Williams' statements regarding FRAs is most likely correct?

• A) Only Statement 2 is correct
• B) Neither statement is correct
• C) Only Statement 1 is correct

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Question: Using the price and predicted MRR rates in Exhibit 1, which of the following is closest to the predicted value of the FRA at the year end?

• A) –$100,000
• B) –-$85,000
• C) –$62,000

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Question: Using the details shown in Exhibit 2, under the terms of the currency swap at the first settlement date Sam Smith would most likely:

• A) pay EUR 150,000
• B) pay USD 130,000
• C) pay EUR 126,050

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Question: Which of the following statements regarding cash flows at the final settlement date for the currency swap outlined in Exhibit 2is most likely correct?

• A) Without knowing the spot rates on the final settlement date, it is impossible to state the cash flows that occur
• B) Sam Smith Inc. will receive USD 40,000,000 plus the USD interest payment Correct
• C) Sam Smith will pay USD 40,000,000 and receive the final USD interest payment

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Question: An index is currently 965 and the continuously compounded dividend yield on the index is 2.3%. What is the no-arbitrage price on a one-year index forward contract if the continuously compounded risk-free rate is 5%.

• A) 991.1
• B) 987.2
• C) 991.4

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Question: An index is currently 876, the risk-free rate (Rf) is 7%, and the dividend yield on the index portfolio is 1.8%. Assuming that these are continuously compounded yields, the price of an 18-month index future is closest to:

• A) 947.1
• B) 943.0
• C) 945.2

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Question: Which of the following statements regarding an option's price is CORRECT? An option's price is:

• A) an increasing function of the underlying asset's volatility Correct
• B) a decreasing function of the underlying asset's volatility
• C) a decreasing function of the underlying asset's volatility when it has a long time remaining until expiration and an increasing function of its volatility if the option is close to expiration

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Question: Two call options have the same delta but option A has a higher gamma than option

• A) larger positive number
• B) larger (negative) number Correct
• C) smaller (negative) number

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Question: How is the gamma of an option defined? Gamma is the change in the:

• A) delta as the price of the underlying security changes Correct
• B) vega as the option price changes
• C) option price as the underlying security changes

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Question: The value of a put option is positively related to all of the following EXCEPT:

• A) risk-free rate
• B) exercise price
• C) time to maturity. Max Perrot, CFA, works for WWF, a mortgage banking company which originates residential mortgage loans. On a monthly basis, WWF issues agency mortgage-backed securities (MBS) backed by their loans. WWF sells the MBS in the open market soon after securitization, but retains the servicing rights to the loans. WWF currently owns the third largest mortgage servicing portfolio in the U.S. Perrot has recently been promoted to Senior Vice President of Asset and Liability Management for WWF. Perrot's new responsibilities encompass hedging WWF's newly created MBS prior to their sale, as well as managing the interest rate exposure on the servicing portfolio. Both types of assets are extremely sensitive to changes in interest rates, though not necessarily in the same manner. Although WWF has retained all of the servicing rights of its loans in the past, they are not opposed to the selling of portions of the portfolio if market conditions are right. WWF's management wants Perrot in his new position to focus primarily on preserving the value of the servicing portfolio through hedging strategies that are cost effective to execute. Also, any hedge strategy used by Perrot must be extremely liquid in the event that a portion of the servicing portfolio is sold and the hedge needs to be unwound. The upper management of WWF anticipates a period of volatility in interest rates, and they have asked Perrot to project expected returns of a hedged position under a variety of interest rates scenarios

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Question: Assume that a three-year semi-annually settled floor with a strike rate of 8% and a notional amount of $100 million is being analyzed. The reference rate is six-month London Interbank Offered Rate (LIBOR). Suppose that LIBOR for the next four semi-annual periods is as follows: Period LIBOR 1 7.5% 2 8.2% 3 8.1% 4 8.7% What is the payoff for the floor for period 1?

• A) $0
• B) $250,000
• C) $500,000

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Question: A LIBOR based floating rate bond combined with a LIBOR based collar (a short position in an interest rate cap and a long position in an interest rate floor both at the same strike rate) is equivalent to a:

• A) pay-fixed swap position
• B) fixed-rate bond
• C) call option on a bond

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Question: Which of the following is most likely a reason why dynamic riskless arbitrage is difficult in real markets?

• A) Securities are subject to insider trading
• B) Continuous rebalancing Correct
• C) Short sale constraints exist. You are interested in derivative products, particularly with a view to identifying arbitrage opportunities. You start with bond futures: The cheapest to deliver (CTD) bond underlying the T-bond futures contract maturing in five months is a 4.6% T-Bond currently priced at $1,002.33 (full price) per $1,000 par. The CTD paid its last coupon four months ago, and its conversion factor is 1.13. The risk free rate is 2.99%

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Question: Which of the following is closest to the no-arbitrage price of the 5-month T-Bond futures contract?

• A) $867.20
• B) $877.47
• C) $976.02

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Question: Comment 1 is best described as:

• A) correct
• B) incorrect as long an interest rate floor should be short an interest rate floor Correct
• C) incorrect as long an interest rate floor should be long an interest rate cap

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Question: Comment 3 can be best described as:

• A) correct
• B) incorrect as it is describing a receiver swaption, not a payer swaption Correct
• C) incorrect as a payer swaption is more valuable if an equivalent swap at the market rate is lower than the strike rate

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Question: Compared to the delta of a long position in a stock, the delta of an at-the-money call option on the stock is most likely to be:

• A) the same
• B) less
• C) greater

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Question: Which of the following is NOT one of the assumptions of the Black-Scholes-Merton option- pricing model?

• A) The yield curve for risk-free assets is fixed over the term of the option Correct
• B) There are no taxes and transactions costs are zero for options and arbitrage portfolios
• C) Early exercise is not allowed.

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Question: Williamson would like to consider neutralizing his Reston equity position from changes in Reston's stock price. Using the information in Tables 3 and 4 how many standard Reston European options would have to be bought/sold in order to create a delta neutral portfolio?

• A) Sell 370,300 call options Correct
• B) Sell 497,141 put options
• C) Buy 497,141 put options

Page 9 | Status: ⏸️ Unattempted

Question: Williamson is very interested in the total return swap. He asks Potter how much it would cost to enter into this transaction. Which of the following is the most likely cost of the swap at inception?

• A) $45,007
• B) $0
• C) $340,885

Page 9 | Status: ⏸️ Unattempted

Question: Potter analyzes alternative hedging strategies to address the risk of the bank's large floating- rate liability. Which of the following is the most appropriate transaction to efficiently hedge the interest rate risk for the floating rate liability without sacrificing potential gains from interest rate decreases?

• A) Sell an interest rate floor and buy an interest rate cap Correct
• B) Sell an interest rate cap
• C) Buy an interest rate cap

Page 9 | Status: ⏸️ Unattempted

Question: Potter is now considering some of the bank's floating rate assets. Which of the following transactions is the most appropriate to minimize the interest rate risk of these assets without sacrificing upside gains?

• A) Buy a floor Correct
• B) Buy a cap
• C) Buy a collar

Page 10 | Status: ⏸️ Unattempted

Question: Regarding options on a stock without dividends, it is:

• A) sometimes worthwhile to exercise calls early but not puts Correct
• B) sometimes worthwhile to exercise puts early but not calls
• C) never worthwhile to exercise puts or calls early. Lowell Wood is using the binomial option-pricing model to price interest rate options. She has obtained the following 2-year, annual rate tree (based on an assumed volatility of interest rates of 25%). Exhibit 1 Wood has been asked help a colleague with the valuation of an interest rate put. The interest rate put option has 2 years to maturity and a strike price of 4.5% and is based on 360 day MRR. The option has a notional principal of $10m

Page 10 | Status: ⏸️ Unattempted

Question: Using the information about the interest rate put and the spot and forward rates in Exhibit 1, which of the following is closest to the value of the put? Assume that the option cash settle at time 2.

• A) $44,250
• B) $64,250
• C) $84,250

Page 11 | Status: ⏸️ Unattempted

Question: Newman's Comment 1 is best described as:

• A) correct
• B) incorrect as to the strike price of the options Correct
• C) incorrect as to the equivalence to a long FRA

Page 12 | Status: ⏸️ Unattempted

Question: Newman's Comment 2 is best described as:

• A) correct
• B) incorrect as buying a floor is not equivalent to buying interest rate put options Correct
• C) incorrect as long floor, short cap would create a pay floating, receive fixed interest rate swap

Page 12 | Status: ⏸️ Unattempted

Question: Mark Roberts anticipates utilizing a floating rate line of credit in 90 days to purchase $10 million of raw materials. To get protection against any increase in the expected MRR yield curve, Roberts should:

• A) write a receiver swaption
• B) buy a payer swaption Correct
• C) buy a receiver swaption

Page 12 | Status: ⏸️ Unattempted

Question: A payer swaption gives its holder:

• A) the right to enter a swap in the future as the floating-rate payer Correct
• B) an obligation to enter a swap in the future as the fixed-rate payer
• C) the right to enter a swap in the future as the fixed-rate payer

Page 13 | Status: ⏸️ Unattempted

Question: Which of the following is NOT one of the assumptions of the Black-Scholes-Merton (BSM) option-pricing model?

• A) There are no transaction costs, regulatory constraints, or taxes
• B) The options valued are European style (early exercise is not allowed)
• C) The yield on the underlying has a known and constant volatility

Page 13 | Status: ⏸️ Unattempted

Question: Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic European call option?

• A) Sell the stock; buy a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond
• B) Buy the stock; sell a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond
• C) Buy the stock; buy a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond

Page 13 | Status: ⏸️ Unattempted

Question: The value of a put option will be higher if, all else equal, the:

• A) exercise price is lower
• B) underlying asset has positive cash flows Correct
• C) underlying asset has less volatility

Page 14 | Status: ⏸️ Unattempted

Question: When an option's gamma is higher:

• A) a delta hedge will be more effective
• B) delta will be higher Correct
• C) a delta hedge will perform more poorly over time

Page 14 | Status: ⏸️ Unattempted

Question: Which of the following is the best approximation of the gamma of an option if its delta is equal to 0.6 when the price of the underlying security is 100 and 0.7 when the price of the underlying security is 110?

• A) 1.00
• B) 0.01
• C) 0.10

Page 14 | Status: ⏸️ Unattempted

Question: Which of the following best describes the implied volatility method for estimated volatility inputs for the Black-Scholes model? Implied volatility is found:

• A) using the most current stock price data Correct
• B) using historical stock price data
• C) by solving the Black-Scholes model for the volatility using market values for the stock price, exercise price, interest rate, time until expiration, and option price

Page 15 | Status: ⏸️ Unattempted

Question: Pete Jenkins makes the following statement about options: "N(d2) is interpreted as the risk-neutral probability that a call option will expire in the money. Similarly, N(-d2) is the risk-neutral probability that a put option will expire in the money." Jenkins is most likely:

• A) incorrect about the risk-neutral probability of put option expiring in the money Correct
• B) correct
• C) incorrect about the risk-neutral probability of call option expiring in the money

Page 15 | Status: ⏸️ Unattempted

Question: If we use four of the inputs into the Black-Scholes-Merton option-pricing model and solve for the asset price volatility that will make the model price equal to the market price of the option, we have found the:

• A) historical volatility
• B) option volatility Correct
• C)

Page 15 | Status: ⏸️ Unattempted

Question: Combining a short position in a stock with a long position in a call option on the stock will produce a payoff pattern equivalent to a:

• A) long position in a put option on the stock
• B) short position in a put option on the stock Correct
• C) risk-free security

Page 16 | Status: ⏸️ Unattempted

Question: Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic riskless pure-discount bond?

• A) Sell a European put option; sell the same stock; buy a European call option Correct
• B) Buy a European put option; sell the same stock; sell a European call option
• C) Buy a European put option; buy the same stock; sell a European call option

Page 16 | Status: ⏸️ Unattempted

Question: Dividends on a stock can be incorporated into the valuation model of an option on the stock by:

• A) subtracting the present value of the dividend from the current stock price Correct
• B) adding the present value of the dividend to the current stock price
• C) subtracting the future value of the dividend from the current stock price

Page 17 | Status: ⏸️ Unattempted

Question: Which of the following statements concerning vega is most accurate? Vega is greatest when an option is:

• A) far out of the money Correct
• B) far in the money
• C) at the money

Page 18 | Status: ⏸️ Unattempted

Question: A stock is priced at 40 and the periodic risk-free rate of interest is 8%. The value of a two- period European call option with a strike price of 37 on a share of stock using a binomial model with an up factor of 1.20 and down factor of 0.833 is closest to:

• A) $9.13
• B) $9.25
• C) $3.57

Page 18 | Status: ⏸️ Unattempted

Question: Using the information in Exhibit 1, Franklin wants to compute the value of the corresponding European call option. Which of the following is the closest to Franklin's answer?

• A) $11.54
• B) $4.78
• C) $5.55

Page 20 | Status: ⏸️ Unattempted

Question: Franklin wants to know how the put option in Exhibit 1 behaves when all the parameters are held constant except the delta. Which of the following is the best estimate of the change in the put option's price when the underlying equity increases by $1?

• A) −$0.37
• B) −$0.33
• C) −$3.61

Page 20 | Status: ⏸️ Unattempted

Question: Franklin wants to know if the option sensitivities shown in Exhibit 2 have minimum or maximum bounds. Which of the following are the minimum and maximum bounds, respectively, for the put option delta?

• A) −1 and 1
• B) There are no minimum or maximum bounds
• C) −1 and 0

Page 21 | Status: ⏸️ Unattempted

Question: Suppose a forward rate agreement (FR

• A) call and a short put on MRR with a strike rate of 8% and six months to expiration
• B) call and a short put on MRR with a strike rate of 8% and twelve months to expiration
• C) put and a short call on MRR with a strike rate of 8% and twelve months to expiration

Page 21 | Status: ⏸️ Unattempted

Question: Early exercise of in-the-money American options on:

• A) futures is sometimes worthwhile but never is for options on forwards Correct
• B) forwards is sometimes worthwhile but never is for options on futures
• C) both futures and forwards is sometimes worthwhile

Page 22 | Status: ⏸️ Unattempted

Question: Bower is a bit puzzled about how to use caps and floors. He wonders how he could benefit both from increasing and decreasing interest rates. Which of the following trades would most likely profit from this interest rate scenario?

• A) Buy at the money cap and sell at the money floor Correct
• B) Sell at the money cap and at the money floor
• C) Buy at the money cap and at the money floor

Page 24 | Status: ⏸️ Unattempted

Question: Bower has studied swaps extensively. However, he is not sure which of the following is the swap fixed rate for a one-year interest rate swap based on 90-day LIBOR with quarterly payments. Using the information in Table 1 and the formula below, what is the most appropriate swap fixed rate for this swap? where

• A) 5.75%
• B) 5.65%
• C) 6.01%. C= 1 −Z4 Z1 + Z2 + Z3 + Z4 Zn = price of n − zero − coupon bond per $ of principal 1 1 + RN

Page 24 | Status: ⏸️ Unattempted

Question: Bower computes the implied volatility of a one year caplet on the 90-day LIBOR forward rates to be 18.5%. Using the given information what does this mean for the caplet's market price relative to its theoretical price? The caplet's market price is:

• A) overvalued
• B) undervalued
• C) undervalued or overvalued

Page 25 | Status: ⏸️ Unattempted

Question: For this question only, assume Bower expects the currently positively sloped LIBOR curve to shift upward in a parallel manner. Using a plain vanilla interest rate swap, which of the following will allow Bower to best take advantage of his expectations? Purchase a:

• A) pay fixed interest rate swap Correct
• B) floating rate bond and enter into a receive fixed swap
• C) receive fixed interest rate swap

Page 25 | Status: ⏸️ Unattempted

Question: The writer of a receiver swaption has:

• A) an obligation to enter a swap in the future as the fixed-rate payer Correct
• B) an obligation to enter a swap in the future as the floating-rate payer
• C) the right to enter a swap in the future as the floating-rate payer. Nathan Detroit, a speculator, has come to you for technical advice regarding the pricing of swaps. He hopes to make big money in the swaps market from the exploitation of pricing discrepancies, but lacks an understanding of the principles underlying the pricing of swaps

Page 25 | Status: ⏸️ Unattempted

Question: Calculate the USD swap fixed rate.

• A) 3.16%
• B) 6.20%
• C) 6.32%

Page 27 | Status: ⏸️ Unattempted

Question: Using the information in Exhibits 1 and 2, which of the following is closest to the amount of the British pound paid on the first settlement date?

• A) £165,000
• B) £187,234
• C) £264,000

Page 27 | Status: ⏸️ Unattempted

Question: Which of the following would create a synthetic call?

• A) Buy the put and the underlying
• B) Sell the put, buy the underlying
• C) Sell the put and the underlying

Page 27 | Status: ⏸️ Unattempted

Question: Which of the following best describes how a payer swap could be replicated using a package of interest rate options?

• A) The swap can be replicated by buying a package of interest rate call options and selling a package of interest rate put options at different strikes
• B) The swap can be replicated by selling a package of interest rate call options and buying a package of interest rate put options at the same strikes
• C) The swap can be replicated by buying a package of interest rate call options and selling a package of interest rate put options at the same strikes

Page 29 | Status: ⏸️ Unattempted

Question: Which of the following best describes how a payer swap could be replicated using interest rate swaptions?

• A) The swap can be replicated by selling a payer swaption and buying a receiver swaption at the same strike
• B) The swap can be replicated by buying a payer swaption and selling a receiver swaption at the same strike
• C) The swap can be replicated by buying a payer swaption and selling a receiver swaption at different strikes

Page 29 | Status: ⏸️ Unattempted

Question: Which of the following comments relating to the Black model valuation of a swaption is the most accurate?

• A) SFR in the formula identified by Lucy is the market swap fixed rate at the expiration of the swaption
• B) N(d2) is likely to be greater than N(d1)
• C) A payer swaption will only be exercised in the market swap fixed rate at expiry is greater than the swaption’s strike price

Page 30 | Status: ⏸️ Unattempted

Question: For a change in which of the following inputs into the Black-Scholes-Merton option pricing model will the direction of the change in a put's value and the direction of the change in a call's value be the same?

• A) Volatility Correct
• B) Exercise price
• C) Risk-free rate

Page 30 | Status: ⏸️ Unattempted

Question: Compared to the value of a call option on a stock with no dividends, a call option on an identical stock expected to pay a dividend during the term of the option will have a:

• A) higher value only if it is an American style option Correct
• B) lower value in all cases
• C)

Page 30 | Status: ⏸️ Unattempted

Question: The value of a European call option on an asset with no cash flows is positively related to all of the following EXCEPT:

• A) exercise price Correct
• B) risk-free rate
• C) time to exercise

Page 31 | Status: ⏸️ Unattempted

Question: A non-dividend-paying option on a stock is most likely to be exercised early if the option is a(n):

• A) European option Correct
• B) call option
• C) put option

Page 31 | Status: ⏸️ Unattempted

Question: A floor on a floating rate note, from the bondholder's perspective, is equivalent to:

• A) owning a series of puts on fixed income securities Correct
• B) writing a series of interest rate puts
• C) owning a series of calls on fixed income securities

Page 31 | Status: ⏸️ Unattempted

Question: Using information in Exhibit 1, the value of $60 strike put option is closest to:

• A) $4.99
• B) $5.86
• C) $7.27

Page 33 | Status: ⏸️ Unattempted

Question: Susan discovers that the fair value for the $55 strike put is in fact $3.85. Which of the following is the most appropriate set of transactions to exploit the mispricing (ignore transaction costs)?

• A) Write a call option, buy a put option, buy one share, borrow the PV of strike Correct
• B) Buy a call option, write a put option, buy one share, borrow the PV of strike
• C)

Page 33 | Status: ⏸️ Unattempted

Question: Using information in Exhibit 2, which of the following statements about assumptions 1 and 2 is most accurate?

• A) Both assumptions are correct Correct
• B) Only one of the two assumptions is correct
• C) Both assumptions are incorrect

Page 34 | Status: ⏸️ Unattempted

Question: Using Exhibit 3, which of the following statements about implications 1 and 2 is most accurate?

• A) Both implications are correct Correct
• B) Both implications are incorrect
• C) Only one of the two implications is correct. Rachel Barlow is a recent graduate of Columbia University with a Bachelor's degree in finance. She has accepted a position at a large investment bank, but first must complete an intensive training program to gain experience in several of the investment bank's areas of operations. Currently, she is spending three months at her firm's Derivatives Trading desk. One of the traders, Jason Coleman, CFA, is acting as her mentor, and will be giving her various assignments over the three month period. One of the first projects Coleman asks Barlow to do is to compare different option trading strategies. Coleman would like Barlow to pay particular attention to strategy costs and their potential payoffs. Barlow is not very comfortable with option models, and knows she needs to be able to fully understand the most basic concepts in order to move on. She decides that she must first investigate how to properly price European and American style equity options

Page 34 | Status: ⏸️ Unattempted

Question: Barlow notices that the stock in Exhibit 1 does not pay dividends. If the stock begins to pay a dividend, how will the price of a call option on that stock be affected? The price of the call option:

• A) may either increase or decrease Correct
• B) will decrease
• C) will increase

Page 36 | Status: ⏸️ Unattempted

Question: Barlow calculated the value of an American call option on the stock shown in Exhibit 2. Which of the following is closest to the value of this call option?

• A) $15.41
• B) $14.84
• C) $15.12

Page 36 | Status: ⏸️ Unattempted

Question: Using the information in Exhibit 2, Barlow computes the value of a European put option. Which of the following is closest to the value of this option?

• A) $1.97
• B) $4.84
• C) $1.41

Page 36 | Status: ⏸️ Unattempted

Question: Barlow notices that the stock in Exhibit 2 does not pay dividends. If the stock starts to pay a dividend, how will the price of a put option on that stock be affected?

• A) Increase Correct
• B) Decrease
• C) Increase or decrease

Page 37 | Status: ⏸️ Unattempted

Question: To create a synthetic short position in a stock, an investor can buy:

• A) a call option on the stock and sell a put option on the stock Correct
• B) a put option on the stock and sell a call option on the stock
• C) both a call option on the stock and a put option on the stock

Page 37 | Status: ⏸️ Unattempted

Question: Which of the following is least likely one of the assumptions of the Black-Scholes-Merton option pricing model?

• A) Changes in volatility are known and predictable Correct
• B) The risk-free rate of interest is known and does not change over the term of the option
• C) The options are European

Page 37 | Status: ⏸️ Unattempted

Question: Which of the following best represents an interest floor?

• A) A portfolio of put options on an interest rate Correct
• B) A put option on an interest rate
• C) A portfolio of call options on an interest rate. Joel Franklin, CFA, has recently been promoted to junior portfolio manager for a large equity portfolio at Davidson Sherman (DS), a large multinational investment banking firm. The portfolio is subdivided into several smaller portfolios. In general, the portfolios are composed of U.S. based equities, ranging from medium to large-cap stocks. Currently, DS is not involved in any foreign markets. In his new position, he will now be responsible for the development of a new investment strategy that DS wants all of its equity portfolios to implement. The strategy involves overlaying option strategies on its equity portfolios. Recent performance of many of their equity portfolios has been poor relative to their peer group. The upper management at DS views the new option strategies as an opportunity to either add value or reduce risk. Franklin recognizes that the behavior of an option's value is dependent upon many variables and decides to spend some time closely analyzing this behavior. He took an options strategies class in graduate school a few years ago, and feels that he is fairly knowledgeable about the valuation of options using the Black-Scholes model. Franklin understands that the volatility of the underlying asset returns is one of the most important contributors to option value. Therefore, he would like to know when the volatility has the largest effect on option value. Upper management at DS has also requested that he further explore the concept of a delta neutral portfolio. He must determine how to create a delta neutral portfolio, and how it would be expected to perform under a variety of scenarios. Franklin is also examining the change in the call option's delta as the underlying equity value changes. He also wants to

Page 38 | Status: ⏸️ Unattempted

Question: Which of the following most accurately describes when the call option delta reaches its minimum bound? The call option reaches its minimum bound when call option is:

• A) at the money Correct
• B) the option's delta has no minimum bound
• C) far out of the money

Page 39 | Status: ⏸️ Unattempted

Question: If the portfolio has 10,000 shares of the underlying stock and he wants to completely hedge the price risk using options, what kind of options should Franklin buy?

• A) Call and put options Correct
• B) Call options
• C) Put options

Page 40 | Status: ⏸️ Unattempted

Question: Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long put options in Exhibit 2 and the stock.

• A) 67.36
• B) 32.64
• C) −32.64

Page 40 | Status: ⏸️ Unattempted

Question: Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long call options in Exhibit 2 and the stock.

• A) 67.36
• B) −67.36
• C) −32.64

Page 40 | Status: ⏸️ Unattempted

Question: Suppose a forward rate agreement (FR

• A) put and a short call on MRR with a strike rate of 6% and two years to expiration Correct
• B) call and a short put on MRR with a strike rate of 6% and two years to expiration
• C)

Page 40 | Status: ⏸️ Unattempted

Question: The one-year call option on Dale Corporation:

• A) is underpriced
• B) is overpriced
• C) may be over or underpriced. The given information is not sufficient to give an answer

Page 41 | Status: ⏸️ Unattempted

Question: Bingly's sentiments towards the Black-Scholes-Merton (BSM) model regarding a lognormal distribution of prices and a variable risk-free rate are:

• A) correct for both reasons
• B) correct concerning the distribution of stocks but incorrect concerning the risk-free rate
• C) incorrect for both reasons

Page 42 | Status: ⏸️ Unattempted

Question: If Bingly forecasts the volatility for a stock and find that it is significantly greater than that implied by the prices of the puts and calls of the stock, he would conclude that:

• A) the puts are overpriced and the calls are underpriced Correct
• B) puts and calls are underpriced
• C) puts and calls are overpriced

Page 42 | Status: ⏸️ Unattempted

Question: All else being equal, the greater the dividend paid by a stock the:

• A) lower the call price and the higher the put price
• B) lower the call price and the lower the put price Correct
• C) higher the call price and the lower the put price. John Fairfax is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. He hires Richard Potter, CFA, a financial adviser from Stan Morgan, LLC, to help him develop investment strategies. Potter suggests a number of interesting investment strategies for Fairfax's portfolio. Many of the strategies include the use of various equity derivatives. Potter explains to Fairfax that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggests that Fairfax consider

Page 42 | Status: ⏸️ Unattempted

Question: Given the information regarding the various Reston stock options, which option will increase the most relative to an increase in the underlying Reston stock price?

• A) European call Correct
• B) American put
• C) American call

Page 44 | Status: ⏸️ Unattempted

Question: Fairfax would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Table 3 how many standard Reston European options would have to be either bought or sold in order to create a delta neutral portfolio?

• A) Sell 334,616 put options Correct
• B) Buy 300,703 put options
• C) Sell 334,616 call options

Page 44 | Status: ⏸️ Unattempted

Question: Fairfax has heard people talking about "making a portfolio delta neutral." What does it mean to make a portfolio delta neutral? The portfolio:

• A) is insensitive to stock price changes Correct
• B) is insensitive to interest rate changes
• C) is insensitive to volatility changes in the returns on the underlying equity. Gina Davalos, CFA is a portfolio manager for the Herron Investments. She is interested in hedging the equity risk of one of her clients, Lou Gier. Gier has 200,000 shares of a stock with the symbol QJX that he believes could take a dive in the next 9 months. Davalos gathers the following information to suggest potential strategies to offset the potential loss. Each option contract is for 100 options. General Information: QJX Current Stock Price $100.00 Risk-free rate 5.0% QJX Dividend Yield 0.0% Time to Maturity (years) 0.75 Option Information: Strike Price $100.00 Value of Call $12.09 Delta on Call Option 0.6081 Value of Put (years) $8.41 Equity Swap Information:

Page 45 | Status: ⏸️ Unattempted

Question: In order to create a delta-neutral hedge using put option contracts, Davalos would most accurately need to:

• A) buy 2,000 contracts
• B) buy 5,103 contracts
• C) sell 510,271 contracts

Page 46 | Status: ⏸️ Unattempted

Question: An equity swap to hedge the equity risk for Gier would result in a net return on the portfolio of a:

• A) fixed rate of 4.5% for the year
• B) variable rate based on the total return of QJX stock Correct
• C) fixed rate of 1.5% per quarter

Page 46 | Status: ⏸️ Unattempted

Question: Based on the futures information, an arbitrage opportunity can be exploited by:

• A) buying the stock QJX, and selling the futures Correct
• B) buying the futures and buying the stock QJX
• C) selling the stock QJX and buying the futures

Page 47 | Status: ⏸️ Unattempted

Question: A stock is priced at 38 and the periodic risk-free rate of interest is 6%. What is the value of a two-period European put option with a strike price of 35 on a share of stock using a binomial model with an up factor of 1.15, a down factor of 0.87 and a risk-neutral up probability of 68%?

• A) $0.57
• B) $0.64
• C) $2.58. Mark Washington, CFA, is an analyst with BIC, a Bermuda-based investment company that does business primarily in the U.S. and Canada. BIC has approximately $200 million of assets under management, the bulk of which is invested in U.S. equities. BIC has outperformed its target benchmark for eight of the past ten years, and has consistently been in the top quartile of performance when compared with its peer investment companies. Washington is a part of the Liability Management group that is responsible for hedging the equity portfolios under management. The Liability Management group has been authorized to use calls or puts on the underlying equities in the portfolio when appropriate, in order to minimize their exposure to market volatility. They also may utilize an options strategy in order to generate additional returns

Page 47 | Status: ⏸️ Unattempted

Question: Which of the following best explains a delta-neutral portfolio? A delta-neutral portfolio is perfectly hedged against:

• A) small price decreases in the underlying asset Correct
• B) all price changes in the underlying asset
• C) small price changes in the underlying asset

Page 48 | Status: ⏸️ Unattempted

Question: Washington is trying to determine the value of a call option. When the slope of the at expiration curve is close to zero, the call option is:

• A) in-the-money Correct
• B) at-the-money
• C) out-of-the-money

Page 49 | Status: ⏸️ Unattempted

Question: BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at $69. A call option on Smith & Oates with a strike price of $70 is selling at $3.50, and has a delta of 0.69 What is the number of call options necessary to create a delta-neutral hedge?

• A) 0
• B) 75,000
• C) 14,785

Page 49 | Status: ⏸️ Unattempted

Question: To the issuer of a floating rate note, a cap is equivalent to:

• A) writing a series of interest rate calls
• B) owning a series of interest rate calls Correct
• C)

Page 49 | Status: ⏸️ Unattempted

Question: A bond analyst decides to use the BSM model to price options on bond prices. This model will most likely be inadequate because:

• A) BSM cannot be modified to deal with cash flows like coupon payments Correct
• B) the price of the underlying asset follows a lognormal distribution
• C) the risk free rate must be constant and known

Page 50 | Status: ⏸️ Unattempted

Question: Cal Smart wrote a 90-day receiver swaption on a 1-year MRR-based semiannual-pay $10 million swap with an exercise rate of 3.8%. At expiration, the market rate and MRR yield curve are: Fixed rate 3.763% 180-days 3.6% 360-days 3.8% The payoff to the writer of the receiver swaption at expiration is closest to:

• A) $0
• B) -$3,600
• C) $3,600

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Question: Which of the following best describes an interest rate cap? An interest rate cap is a package or portfolio of interest rate options that provide a positive payoff to the buyer if the:

• A) T-Bond futures exceeds the strike price
• B) reference rate exceeds the strike rate Correct
• C) reference rate is below the strike rate

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Question: The price of a June call option with an exercise price of $50 falls by $0.50 when the underlying non-dividend paying stock price falls by $2.00. The delta of a June put option with an exercise price of $50 closest to:

• A) –0.25
• B) 0.25
• C) –0.75

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Question: The delta of an option is equal to the:

• A) dollar change in the stock price divided by the dollar change in the option price Correct
• B) dollar change in the option price divided by the dollar change in the stock price
• C) percentage change in option price divided by the percentage change in the asset price

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