BFC5915 - Options Derivatives
You are given the following information on shares and options on Sunless Ltd. Sunless shares are currently trading at $10.30. You construct a portfolio of 200 long call options at an exercise price of $9.50 and 100 long call options at an exercise price of $10.50 over Sunless shares. Each call option is over one share. (FIND INFO ON GOOGLE DOC) 1. The cost to set the portfolio up is $ (how much??). Give answer to two decimals. 2. The delta of your portfolio of long call options is (??). Give answer to two decimals. 3. To construct a delta neutral portfolio you add shares to the portfolio of long call options. You must add a (short/long?) position in (how many??) shares. round to the nearest number.
1. Cost is 200 × 1.4439 + 100 × 0.8975 = $378.5332=$378.53 2. Delta(portfolio) = 200 × 0.7274 + 100 × 0.5530 = 200.7865 = 200.79 3. The portfolio of long call options has a positive delta. To make the portfolio delta neutral you must short (sell) shares. You need to sell 201 shares (rounding up).
You operate a business in Australia that frequently trades with partners in China. As a result, you often receive payments denominated in Renminbi (RMB), and occasionally you pay bills in RMB. This exposes you to foreign exchange risk, therefore you make use of forward contracts to manage this risk. The spot exchange rate between AUD and RMB is RMB1.0000 = AUD0.2650. The riskfree rates of interest in Australia and China are 2% and 5% respectively 1. The 6-month forward rate for the delivery of RMB six months' from today is RMB1.0000=AUD (how much??). Give your answer correct to four decimal places. 2. Suppose that the forward exchange rate you observe is less than the answer you calculated in part 1.Then to make arbitrage profit you should: 1. Borrow AUD, convert it to RMB at the spot rate, invest the resulting RMB in China for 6 months, and enter a six-month forward contract to sell the accumulated RMB 2. Borrow AUD and convert it to RMB at the forward rate to make a profit 3. Borrow RMB and convert to AUD at the forward rate to make a profit 4. Borrow RMB, convert it to AUD at the spot rate, invest the accumulated AUD in Australia for 6 months, and enter a six-month forward contract to sell the accumulated AUD
1. The 6 month forward rate is F=0.2650exp((0.02-0.05)*0.5)= 0.2611 2. The forward rate is too low. Buy the forward (buy RMB under the 6 month forward contract) and sell the spot (sell RMB spot). The strategy therefore is to borrow RMB for 6 months, sell the RMB immediately in the spot market (exchange RMB for AUD), invest the resulting AUD for 6 months, and then sell the accumulated AUD under the 6 month forward contract (that is, buy RMB forward). This will result in a riskless profit. (option 4)
Today the spot rate between US dollars (USD) and Australian dollars (AUD) is USD1=AUD1.6290. An exporter of goods in Australia will sell goods to a US counterpart and will receive a payment of USD2,000,000 in 6 months time. The current 6-month forward rate is USD1=AUD1.6249. 1. The Australian exporter is exposed to the risk of the AUD (depreciating/ appreciating?) 2. Assume that the Australian exporter enters a 6-month forward contract to hedge this risk. If the spot rate is USD1=AUD1.6010 in 6 months time, the Australian exporter will make a (profit/loss?) when the forward contract is closed.
1.The exporter must sell USD2,000,000 (exchange USD for AUD) in 6 months time. Current exchange rate is USD1=AUD1.6290. If the AUD appreciates then 1USD will be exchanged for less AUD, which won't be good for the exporter. Currently 1USD can be exchanged for 1.6290AUD, and so USD2,000,000 will be exchanged for AUD3,258,000. If the AUD appreciates let's say 1USD=0.6249USD then USD2,000,000 will be exchanged for AUD3,202,000. So if the AUD appreciates the USD are being exchanged for less AUD and the exporter suffers a loss in revenue. 2.As shown above the exporter has locked into a forward rate of USD1=AUD1.6249. If the spot exchange rate is USD1=AUD1.6010 in 6 months then the AUD has appreciated. The exporter therefore makes a profit when the forward contract is closed. What's the profit on the forward contract? Answer: (2,000,000*1.6429)-(2,000,000*1.6010)= +AUD47,800
A company enters into a long futures contract to buy 1,000 barrels of oil for $60 per barrel. The initial margin is $6,000 and the maintenance margin is $4,000. What oil futures price will result in a margin account balance of $9838?
Answer: 63.84 Each $1 movement in the oil price results in a $1,000 movement in the margin account. You are given the margin account balance. You need to divide it by 1000 to calculate the price movement, and then either subtract it or add it to the original oil price.
A short put option when exercised against the writer results in the writer buying the underlying shares at the strike price. A long call option when exercised results in the holder buying the underlying shares at the strike price. Therefore a short put option and a long call have the same net payoff diagram. Select one: a. True b. False
Correct Answer: False A long call option is exercised at the choice of the holder for a profit when the share price rises above the strike price. A short put is exercised against the writer. The writer must buy at the strike price when the shares are trading at a lower price in the market. The writer makes a loss. The net payoff diagrams are not the same. Draw them for yourself.
A trader creates a spread by buying a 6-month call option with a $25.00 strike price for $7.80 and selling a 6-month call option with a $30.00 strike price for $4.10. The initial cost to set up the strategy is (how much?) .Give your answer correct to two decimal places. The breakeven share price for the strategy is $(how much?) . Give your answer correct to two decimal places, or your answer will be incorrect. This strategy is called a (bear/bull)-spread.
Correct Answers are: - 3. 70 - 28. 70 - bull spread
A portfolio contains only long (bought) call options. The gamma of the portfolio is negative. Select one: a. True. b. False
Gamma for a long call is always positive, so gamma for a portfolio of long call options will be positive Gamma for a short call is always negative so gamma for a portfolio of short call options will be negative The correct answer is 'False'.
One-year European call and put options on an asset are worth $5 and $3 respectively when the strike price is $25 and the one-year risk-free rate is 4%. What is the six-month futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.) Select one: a. $26.02 b. $26.50 c.$27.04 d. $25.65
Put call parity is c+ Ke-rT =p+ F0e-rT Hence F0=K+(c-p)erT =25+(5-3)e0.04×0.5= $27.04 The correct answer is: $27.04
The price of a stock is $20.00. The riskfree rate for all maturities is 4%. A put option with six months to maturity and a strike price of $20.00 is trading at $1.00. The price of the call option with the same strike price and maturity, correct to two decimal places is Select one: a. $1.47 b. $1.42 c. $1.40 d. $1.00
Put-call parity states that C=P+S-Kexp(-rT)=1.00+20.00-20.00*exp(-0.04*0.5)=1.3960 or $1.40 correct to 2 decimal places The correct answer is: $1.40
The option prices derived from a risk-neutral valuation approach and the replicating portfolio approach are different. Select one: a. True. b. False
Risk-neutral valuation produces a valuation that is correct in all situations not just those where investors are risk-neutral. The expected return on all investments is assumed to be the risk-free rate and the risk- free rate is used to discount expected payoffs. It gives exactly the same option price as the replicating portfolio approach. The correct answer is 'False'.
We intend to value a European call option with a strike price X=$10 and T=1 year to expiry, using a one- step binomial model, with the following parameters: u=1.2, d=0.8333. The risk-free interest rate (continuously compounded) is 3% per annum. (BINOMIAL ON GOOGLE DOC) 1. The value of the call option in the up state at time 1 is (how much?) . Give your answer correct to two decimal places. The value of the call option in the down state at time 1 is (how much?) . Give your answer correct to two decimal places. 2. The portfolio that replicates the payoff on the call option is a (long/short) position in (how many?) units of shares and a (long/short?) position of $ (how much) in a riskless bond (that is a borrowing). Give your numerical answers to this part of the question correct to three decimal places. 3. Hence the value of the call option at time 0 is (how much?). Give your answer correct to two decimal places.
S0=10, Su=12, Sd = 8.33, Cu = 2, Cd = 0, r=0.03 Calculate Δ = (Cu-Cd)/(Su-Sd)=(2-0)/(12-8.333)=0.5454=0.545 Calculate B=(uCd-dCu)/[(u-d)exp(0.05*1)]=(1.2*0-0.8333*2)/[0.3667*1.0305]=-4.4105=-4.441 C=ΔS+B = 0.5454*10-4.4105=1.0435 or 1.04 to two decimal places
Using the BSM model, the delta for a European put option on a non-dividend paying stock is defined as: Select one: a. N(d1) b. 1 - N(d1) c. N(d2)-1 d. -N(-d1)
The BSM model gives the value of a European put option on a non-dividend paying stock as PE=-S0 N(-d1 )+Xe(-rT) N(-d2 ) where N(-d1) and N(-d2) are normal distribution functions and give the area under the normal curve from -∞ up to -d1 or -d2 respectively. -N(-d1) gives the delta of the put option. This could also be written as -N(-d1)= - (1-N(d1)) = N(d1) -1 The correct answer is: -N(-d1)
On March 1 a commodity's spot price is $60 and its August futures price is $62. On July 1 the spot price is $63 and the August futures price is $62.50. A company entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its futures position on July 1. What is the effective price (after taking account of hedging) paid by the company? Select One: a. 60.50 b. 63.50 c. 59.50 d. 62.50
The correct answer is: $62.50 The user of the commodity takes a long futures position. The gain on the futures is 62.50−62 or $0.50. The effective price paid is therefore the spot price minus the gain on the futures which is, 63−0.50 or $62.50. This can also be calculated as the March 1 futures price (=62) plus the basis on July 1 (=0.50).
You enter a long position in a European-style call option which has a strike price of $26. The option premium paid to enter this position is $5. At expiry, the underlying stock price is $34. What is your net payoff on this long call? Select one: a. -$8 b. -$5 c. -$3 d. +$3 e. +$5 f. +$8
The correct answer is: +$3
USD stands for US dollars, EUR stands for EURO and SEK stands for Swedish Kroner. A US-based company exports to Sweden and needs to hedge the receipt of SEK in 3 months time. The standard deviation of quarterly changes in the USD/SEK spot rate is 0.10, the standard deviation of quarterly changes in the forward rate of USD/EUR is 0.20, and the correlation between the two changes is 0.9. What hedge ratio should be used to hedge the price of Swedish Kroner? Select one: a. 0.18 b. 0.45 c. 1.8 d. 0.90
The correct answer is: 0.45 The optimal hedge ratio is 0.9 X (0.1/0.2)=0.45
The spot price of an investment asset that provides no income is $79 and the risk-free rate for all maturities (with continuous compounding) is 10%. What is the 3-year forward price?
The correct answer is: 106.64 F=S*exp(r*T) where S is the spot price, r is the risk-free interest rate (measured as a decimal) and T is the time to maturity measured in years.
A Binomial tree has a branch length of 2 months (δt = 0.1667). If the proportional up and down movements are u = 1.1000 and d = 0.9091 respectively, what is the volatility (σ) of the underlying asset? Select one: a. 23.35% b. 57.19% c. 10.14% d. Impossible to determine without knowing how may steps in the Binomial tree.
The correct answer is: 23 35%
Which of the following statement is false? Select one: a. A European call price always has positive time value b. A European put price always has positive time value c. An American call option on a non-dividend paying stock always has positive time value d. An out-of-the money call option means that the stock price is less than the exercise price
The correct answer is: A European put price always has positive time value
The spot exchange rate between the Australian dollar (AUD) and the US Dollar (USD) is USD 1.0000 = AUD 1.3793. Which of the following reflects a strengthening of the AUD? Select the best answer Select one: a. USD 1.0000 = AUD 1.4300 b. USD 1.0000 = AUD 1.2900 c. AUD 1.0000= USD 0.7000 d. AUD 1.000 = USD 0.7400 e. Both a. and c. reflect a strengthening AUD f. Both b. and d reflect a strengthening AUD
The correct answer is: Both b. and d reflect a strengthening AUD
Suppose we expect the price of ABC stock to be very volatile and we consider a downward movement in the stock price to be more likely than an upward movement. Which of the following is the best strategy? Select one: a. Buy one share and one put b. Sell two puts and buy one call c. Buy one call and sell two puts d. Buy one call and two puts
The correct answer is: Buy one call and two puts. It is a long strap. The slope of the payoff to the left of X is steeper. So the trader expects it's more likely for the share price to decrease than increase, and would make more money on the decrease. It consists of one call option and two put options at strike price K.
When the stock price increases with all else remaining the same, which of the following is true? Select one: a. Calls increase in value while puts decrease in value b. Both calls and puts decrease in value c. Puts increase in value while calls decrease in value d. Both calls and puts increase in value
The correct answer is: Calls increase in value while puts decrease in value Stock price increases cause the values of calls to increase and the values of puts to decline.
A company has a $10 million portfolio with a beta of 1.1. The futures price for a contract on a market equity index is 1000. The multiplier on the index is $25. What trade is necessary to hedge the portfolio? Select One: a. Short 44 contracts b. Long 44 contracts c. Short 440 contracts d. Long 440 contracts
The correct answer is: Short 440 contracts Need to short the index futures. Number of con tracts =beta X (amount to be hedged)/(value of one contract)=01.1 X $10,000,000/(1000 X $25) = 440
A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 4% and the nine-month rate is 4.5%. If the rate that can be locked in for the period between six months and nine months using an FRA is 6%, which of the following statements is true? (all rates are continuously compounded) Select one: a. The arbitrage-free FRA rate is 5.5% but there is no arbitrage profit that can be made because the interest rates are in equilibrium. b. The arbitrage-free FRA rate covering the period from 6 to 9 months is 5.5%. The bank can make an arbitrage profit by investing at the FRA rate, borrowing for 9 months at 4.5% and investing for6 months at 4%. c. The arbitrage-free FRA rate covering the period from 6 months to 9 months is 5.5%. The bank can make arbitrage profit by borrowing against the quoted FRA rate, borrowing for 6 months at 4% and investing for 9 months at 4.5%.
The correct answer is: The arbitrage-free FRA rate covering the period from 6 to 9 months is 5.5%. The bank can make an arbitrage profit by investing at the FRA rate, borrowing for 9 months at 4.5% and investing for 6 months at 4%.
Which of the following is true about a short forward contract Select one: a. The contract is worth zero if the price of the asset rises after the contract has been entered into b. The contract becomes more valuable as the price of the asset rises c. The contract becomes more valuable as the price of the asset declines d. The contract is worth zero if the price of the asset declines after the contract has been entered into
The correct answer is: The contract becomes more valuable as the price of the asset declines Recall the graph of a short forward contract. When the price of the underlying declines, you can sell at the forward price which is higher. The more the underlying price falls the more valuable your short forward contract.
An investor shorts a futures contract on an asset when the futures price is $1,000. Each contract is on 100 units of the asset. The contract is closed out when the futures price is $900. Which of the following is true Select one: a. The investor has made a loss of $1,000 b. The investor has made a gain of $1,000 c. The investor has made a loss of $10,000 d. The investor has made a gain of $10,000
The correct answer is: The investor has made a gain of $10,000 An investor who shorts (has a short position) makes a gain when th`e futures price decreases. Gain = ($1000 - $900) x 100 = $10,000
An investor buys a futures contract on the SPI futures when the index is at 6000. The multiplier on the index is $25. The investor closes out the futures contract when the futures index is at 6400. Which of the following is true? Select one: a. The investor has made a gain of $10,000 b. The investor has made a loss of $1,000 c. The investor has made a gain of $1,000 e. The investor has made a loss of $10,000
The correct answer is: The investor has made a gain of $10,000 Each index point is worth $25. If the index rises 400 points to 6400, this is a gain on a long index futures position of Gain = ($25) x 400 = $10,000
The price of a stock is $60.00. A trader buys 2 put option contracts on the stock with a strike price of $58.00 when the option price is $4.00. When does the trader make a net profit? Select one: a. When the stock price is below $58.00 b. When the stock price is below $54.00 c. When the stock price is below $50.00 When the stock price is below $60.00
The correct answer is: When the stock price is below $54.00 The net payoff for a put option means that the stock price must fall below the strike price by the amount paid for the put option. In this case the put option cost $4.00 so the stock price must fall to $58.00-$4.00 = $54.00 for the trader to make a net profit.
Some time ago you entered one long contract on Jul-21 Eastern Australian Wheat futures at $302 per tonne. It is now May 2021 and you wish to close out your long futures position. Which of the following is TRUE? a. You close out your long futures contract by entering one short Jul-21 wheat contract. b. You close out your long futures contract by entering two long Jul-21 wheat contracts. c. You cannot close out your long futures position early. You must wait until the expiry date of the July contract. d. You close out your long futures contract by entering two short Jul-21 wheat contracts. e. You close out your long futures contract by entering one long Jul-21 wheat contract.
The correct answer is: You close out your long futures contract by entering one short Jul-21 wheat contract.
A European-style call option on a stock has a strike price of $31. You enter a long call option position. At expiry, the underlying stock price is $28. What is your gross payoff on this long call? Select one: a. Zero, since you won't exercise the option. b. -$3 c. +$3 d. It is impossible to determine whether the call will be exercised without knowing the option premium paid for the long call.
The correct answer is: Zero, since you won't exercise the option.
A European-style put option on a stock has a strike price of $22. You enter a long put option position. At expiry, the underlying stock price is $26. What is your gross payoff on this long put? Select one: a. +$4 b. -$4 c.Zero, since you won't exercise the option. d. It is impossible to determine whether the put will be exercised without knowing the option premium paid for the long put.
The correct answer is: Zero, since you won't exercise the option.
A company enters into a long futures contract to buy 50,000 units of a commodity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is (are) the futures price(s) per unit below which there will be a margin call? You must find all prices below which there will be margin call. Select one or more: a. 70 cents b. 66 cents c. 68 cents. d. 72 cents
The correct answers are: 68 cents, 66 cents There will be a margin call when more than $1,000 has been lost from the margin account so that the balance in the account is below the maintenance margin level. Because the company is long, each one cent decline in the price leads to a loss or 0.01×50,000 or $500. A greater than 2 cent decline in the futures price will therefore lead to a margin call. The futures price is currently 70 cents. When the price declines below 68 cents there will be the first margin call. If the price continues to decline there will another margin call below 66 cents.
Alpha Fund Ltd will have a sum to invest short-term in 6 months' time and wishes to hedge against a fall in interest rates. To hedge against a fall in interest rates, Alpha could (choose all correct answers): Select one or more: a. Buy Bank Bill Futures with maturity date in 6 months' time b. Sell a FRA that settles in 6 months' time c. Buy a FRA that settles in 6 months' time d. Sell Bank Bill Futures with maturity date in 6 months' time
The correct answers are: Sell a FRA that settles in 6 months' time, Buy Bank Bill Futures with maturity date in 6 months' time
An interest rate is 6% per annum with quarterly compounding. What is the equivalent rate with continuous compounding? a. 6.21% b. 5.83% c. 5.96% d. 6 18%
The equivalent rate with continuous compounding is 4*ln(1+0.06/4) = 0.0596 or 5.96%. The correct answer is: 5.96%
A stock price is $100. Volatility is estimated to be 25% per year. What is an estimate of the standard deviation of the change in the stock price in 3 months? Select one: a. $6.25 b. $12.50 c. $14.43 d. $8.33
The estimate is 100 × 0.25 × √(1/4) = $12.50 The correct answer is: $12.50
What is the value of a European put futures option where the futures price is 50, the strike price is 52, the risk-free rate is 5%, the volatility is 20% and the time to maturity is three months? Select one: a. 51.35N(-0.342)-49.38N(-0.442) b. 52N(0.342)-50N(0.442) c. 51.35N(0.442)-49.38N(0.342) d. 52N(-0.342)-50N(-0.442)
The formula is given by p = -F0e-rTN(-d1)+Ke-rTN(-d2). ^use formula from ppt and not this one The only possible answer that matches is 51.35N(0.442)-49.38N(0.342). The correct answer is: 51.35N(0.442)-49.38N(0.342)
Which of the following is true for the party paying fixed in a newly negotiated interest rate swap when the yield curve is downward sloping? Select one: a. The early forward contracts underlying the swap have a positive value and the later ones have a negative value b. The early forward contracts underlying the swap have a negative value and the later ones have a positive value c. The swap is designed so that all forward contracts have zero value d. Sometimes a. is true and sometimes b. is true
The forward contracts are contracts where fixed is paid and floating is received. They can be valued assuming that forward rates are realized. Forward rates decrease with maturity. This means that the value of the forward contracts decrease with maturity. The total value of the forward contracts is zero. This means that the value of the early contracts is positive and the value of the later contracts is negative. The correct answer is: The early forward contracts underlying the swap have a positive value and the later ones have a negative value
The zero coupon curve is given as follows: (IMAGE ON GOOGLE DOC) The forward rates are calculated using continuous compounding. The three year forward one year rate f(3,4) is equal to Select one: a. 5.21% b. 5.01% c. 5.20% d. 5.00%
The forward rate f(3,4) is calculated as (0.043×4-0.04×3)/(4-3)=0.052 The correct answer is: 5.20%
Which of the following statements about forward rates is true? a. The forward rates can be calculated from the zero coupon yield curve. b. If the zero coupon curve is upward sloping, then the forward rate from year 1 to year 2, f(1,2), is greater than the two-year spot rate. c. In a downward sloping zero coupon curve then the forward rate from year 2 to year 3, f(2,3), is less than the 3-year spot rate. d. All of the statements a, b, c, are true
The forward rate is the interest rate implied by the current term structure for future periods of time. It is calculated from the zero coupon yield curve. When the yield curve is upward sloping the forward rate for year n is higher than the spot rate for year n. When the yield curve is downward sloping the forward rate for year n is lower than the spot rate for year n. The correct answer is: All of the statements a, b, c, are true
Today the spot rate between US dollars (USD) and Australian dollars (AUD) is USD1=AUD1.6290, and the current spot price of gold is USD1,500 per ounce. You are an Australian gold miner and expect to have 10,000 ounces of gold ready for sale in 3 months time. You decide not to hedge your exposure. When you are ready to sell the gold in 3 months, the spot price of gold is USD1,300 per ounce, and the spot exchange rate is USD1 = AUD1.5000. 1. The Australian gold miner is exposed to the risk of the gold price (falling/rising??) 2. The Australian gold miner is exposed to the risk of the USD (appreciating/ depreciating??) 3. In three months time, when the Australian gold miner sells 10,000 ounces of gold at the spot price for gold, the revenue received in AUD will be AUD (how much ??) million. Give your answer in millions to two decimal places or your answer will be incorrect.
The gold miner needs to sell gold in 3 months time. If the gold price falls then the gold miner gets less revenue in USD. If the USD depreciates then the USD will convert to less AUD. 10,000X1,300 is the revenue in USD. Convert this to AUD gives 10,000X1,300X1.5=19,500,000 or 19.50 million to 2 decimal places
Company X and Company Y have been offered the following rates: (IMAGE ON GOOGLE DOC) Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, what is company X's effective borrowing rate? Select one: a. 3-month LIBOR minus 30bp b. 3-month LIBOR minus 60 bp c. 3.3% d. 3.0%
The interest rate differential between the fixed rates is 100 basis points. The interest rate differential between the floating rates is 40 basis points. The difference between the interest rates differentials is 100 - 40 = 60 basis points. This is the total apparent gain from the swap to the two sides. Since the benefits are shared equally company X should be able to borrow at 30 bp less than it is currently offered in the floating rate market, i.e., at LIBOR minus 30 bp. The correct answer is: 3-month LIBOR minus 30bp
The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? Select one: a. $4.98 b. $3.98 c. $5.00 d. $5.98
The lower bound in S0 − Ke-rT. In this case it is 30 - 25e-0.04×1 = $5.98. The correct answer is: $5.98
An American-style put option written on ABC has one month to expiry and a strike price of $8.50. It is currently trading at $0.55. ABC shares are trading at $7.80. The riskless rate of interest is 4%. To make arbitrage profits you should: Select one: a. Arbitrage profits cannot be made. b. Buy the put option immediately because it is underpriced. c. Buy the put option, buy ABC shares on market, immediately exercise the right to sell the ABC shares, for arbitrage profit of $0.15. d. Buy the shares on market and sell the put option, using borrowed funds of $7.25. The arbitrage profit at maturity is greater than $1.25.
The lower bound on the American-style put option is PA≥max[0, X - S0]. Substitute the values in. The lower bound is $0.70. The put option price is below the lower bound Strategy to make arbitrage profit is to Enter long put option = -0.55 Immediately buy shares on market = -7.80 Immediately exercise right to sell shares = +8.50 Arbitrage profit= +0.15 The correct answer is: Buy the put option, buy ABC shares on market, immediately exercise the right to sell the ABC shares, for arbitrage profit of $0.15.
An exchange rate is 1.6855 (1 unit of foreign (base) currency = 1.6855 units of domestic (terms) currency). The nine-month domestic risk-free interest rate is 4% per annum and the nine-month foreign risk-free interest rate is 6% per annum (both expressed with continuous compounding). What is the nine- month forward rate? Select one: a. 1.7109 b. 1.6604 c. 1.7024 d. 1.6687
The nine-month forward rate is 1.6855e(0.04−0.06)×0.75=1.6604 The correct answer is: 1.6604
A portfolio manager in charge of a portfolio worth $80 million is concerned that stock prices might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $80 million. The index is currently standing at 4000. The multiplier on options on the index is $10. If the portfolio has a beta of 1.3 what position in put options is required to insure the portfolio at its current level (ignoring the option premium)? Select one: a. Short 26000 contracts b. Short 2600 contracts c. Long 2600 contracts d. Long 26000 contracts
The number of contracts required is β×80,000,000/(4000 × 10 )=2,600. A long put position is required because the contracts must provide a positive payoff when the market declines. The correct answer is: Long 2600 contracts
An electric car manufacturer needs to buy 10,200 ounces of palladium in three months time (October) and needs to hedge it. The closest contract is gold futures traded on the CME, with October expiry, where each contract is on 100 ounces of gold. The standard deviation of changes in palladium is 0.45. The standard deviation of changes in gold futures is 0.24, and the coefficient of correlation between the two changes is 0.60. The optimal hedge ratio for a three-month contract is (??) Answer. Give your answer correct to three decimal places. The electric car manufacturer should take a (long/short?) position on (how many??) contracts on gold futures on the CME for October delivery. Give your answer as a whole number of contracts.
The optimal hedge ratio is 0.60 x 0.45/0.24 = 1.1250 = 1.125 correct to three decimal places. Therefore take a long position on 10200*1.125/100=114.75 or 115 contracts
An investor is short a covered call. The current stock price is $50, strike price for the option is $52.50, and the option premium is $3.50. The investor will start making a profit on this short covered call as long as the stock price at maturity is Select one a. :the investor will always make a profit from this strategy b. less than $49.00 c. less than $46.50 d. less than $50 d. less than $52.50
The profit for a short covered call (short stock and long call) is If ST > 52.50, profit = -(ST - S0) +(ST-K) - C = +50 -52.50 - 3.50 = -$6.00 If ST <= 52.50, profit = -(ST - S0 )- C = -ST +50 - 3.50 = -ST +46.50. The investor will start making a profit as long as stock price at maturity is less than $46.50. The correct answer is: less than $46.50
An investor uses a long protective put strategy. The current stock price is $21.00, the strike price for the option is $19.00, and the option premium is $1.50. The investor will start making a profit on this protective put strategy as long as the stock price at maturity is Select one: a. Greater than $21.00 b. Greater than $19.00 c. The investor will always make a profit from this strategy d. Greater than $22.50
The profit for protective put is If ST > 19, profit = ST - S0 - p = ST - 21 - 1.50 = ST - 22.50 If ST <= 19, profit = K - S0 - p = 19 - 21 - 1.50 = -3.50. The investor will start making a profit as long as stock price at maturity is greater than 22.50 The correct answer is: Greater than $22.50
The yield curve is flat at 4% per annum. What is the value of an FRA where the holder receives interest at the rate of 6% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semiannually. Select one: a. $9.25 b. $9.06 c. $9.61 d. $18.11
The value of the FRA is the value of receiving an extra 0.5×(0.06−0.04)×1000 = $10 in 2.5 years. This is 10/((1.02)^5) = $9.06. The correct answer is: $9.06
When LIBOR is used as the discount rate: a. A swap is worth zero immediately before a payment date b. The floating rate bond underlying a swap is worth par immediately after a payment date c. The floating rate bond underlying a swap is worth par immediately before a payment date d. A swap is worth zero immediately after a payment date
The value of the floating rate bond underlying an interest rate swap is worth par immediately after a swap payment date. This result is used when the swap is valued as the difference between two bonds. The correct answer is: The floating rate bond underlying a swap is worth par immediately after a payment date
When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate (continuously compounded) is 6%, the volatility is 30% and the time to maturity is 3 months, which of the following is the price of a European put option on the stock? Select one: a. 19.70N(-0.025) - 20N(-0.175) b. 19.70N(-0.175) - 20N(-0.025) c. 20N(-0.175) - 19.70N(-0.025) d. 20N(-0.025) - 19.70N(-0.175)
Use the spreadsheet: It's a put option. -d1=-0.175. -d2=-0.025. The only answer that fits is 19.70N(-0.025) - 20N(-0.175). Also 20*exp(-0.06*.25)=19.70 to two decimal places. The correct answer is: 19.70N(-0.025) - 20N(-0.175)
A company can borrow funds for five years at LIBOR plus 60 basis points. The five-year swap rate is 2%. What fixed rate of interest can the company borrow at by using the swap? Select one: a. 2.4% b. 1.4% c. 2.0% d. 2.6%
When the company borrows at LIBOR plus 0.6% and then enters into a swap where it receives LIBOR and pays 2%, overall it pays 2.6% per annum. Note that it is the offer rate that will apply to the swap. The correct answer is: 2.6%
When we apply the binomial option pricing model to calculate an option value, one approach is to use risk neutral valuation, where we calculate the risk neutral probability. We have constructed a 6 period binomial tree to price a 12 month put option. The tree parameters are u =1.130, d = 0.885, r = 0.04. The risk neutral probability correct to three decimal places is: Select one: a. 0.552 b, 0.483 c. 0.636 d. 0.497
p=(erΔt-d)/(u-d). Substitute the values in. Δt=2/12 The correct answer is: 0.497
