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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

On July 1, 2011, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2012. On September 1, 2011, it enters into a forward contract to sell 10 million Japanese yen on
In the 1980s, Bankers Trust developed index currency option notes (ICONS). These are bonds in which the amount received by the holder at maturity varies with a foreign exchange rate. One example was
Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price
“Options and futures are zero-sum games.” What do you think is meant by this?
The Chicago Board of Trade offers a futures contract on long-term Treasury bonds.Characterize the traders likely to use this contract.
A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $0.0080 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract
A US company expects to have to pay 1 million Canadian dollars in 6 months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.
A company knows that it is due to receive a certain amount of a foreign currency in 4 months. What type of option contract is appropriate for hedging?
A trader writes a December put option with a strike price of $30. The price of the option is $4. Under what circumstances does the trader make a gain?
It is May and a trader writes a September call option with a strike price of $20. The stock price is $18 and the option price is $2. Describe the trader’s cash flows ifthe option is held until
Suppose that a June put option to sell a share for $60 costs $4 and is held until June.Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit?
Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March. Under what circumstances will the holder ofthe option make a profit? Under what circumstances will the
Explain why a futures contract can be used for either speculation or hedging.
When first issued, a stock provides funds for a company. Is the same true of a stock option? Discuss.
Suppose that you own 5,000 shares worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next 4 months?
You would like to speculate on a rise in the price of a certain stock. The current stock price is $29 and a 3-month call with a strike price of $30 costs $2.90. You have $5,800 to invest. Identify
What is the difference between the over-the-counter market and the exchange-traded market? What are the bid and offer quotes of a market maker in the over-the-counter market?
Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself
A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the
An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.4000 US dollars per pound. How much does the investor gain or lose if the
Explain carefully the difference between selling a call option and buying a put option.
What is the difference between entering into a long forward contract when the forward price is $50 and taking a long position in a call option with a strike price of $50?
Explain carefully the difference between hedging, speculation, and arbitrage.
What is the difference between a long forward position and a short forward position?
In the oil example considered in Section 31.6: (a) What is the value of the abandonment option if it costs $3 million rather than zero? (b) What is the value of the expansion option if it costs $5
Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in
A driver entering into a car lease agreement can obtain the right to buy the car in 4 years for $10,000. The current value of the car is $30,000. The value of the car, S, is expected to follow the
The market price of risk for copper is 0.5, the volatility of copper prices is 20% per annum, the spot price is 80 cents per pound, and the 6-month futures price is 75 cents per pound. What is the
Suppose that the LIBOR zero rate is flat at 5% with annual compounding. In a 5-year swap, company X pays a fixed rate of 6% and receives LIBOR. The volatility of the 2-year swap rate in 3 years is
Explain why a plain vanilla interest rate swap and the compounding swap in Section 30.2 can be valued using the "assume forward rates are realized" rule, but a LIBOR-in- arrears swap in Section 30.4
Calculate the total convexity/timing adjustment in Example 30.3 of Section 30.4 if all cap volatilities are 18% instead of 20% and volatilities for all options on 5-year swaps are 13% instead of 15%.
What is the value of a 5-year swap where LIBOR is paid in the usual way and in return LIBOR compounded at LIBOR is received on the other side? The principal on both sides is $100 million. Payment
What is the value of a 2-year fixed-for-floating compound swap where the principal is $100 million and payments are made semiannually. Fixed interest is received and floating is paid? The fixed rate
Calculate all the fixed cash flows and their exact timing for the swap in Business Snapshot
In the flexi cap considered in Section 29.2 the holder is obligated to exercise the first Nin-the-money caplets. After that no further caplets can be exercised. (In the example, N=5) Two other ways
In an amual-pay cap, the Black volatilities for caplets with maturities 1, 2, 3, and 5 yours are 18%, 20%, 22%, and 20%, respectively. Estimate the volatility of a 1-year forward rate in the LIBOR
Prove equation (29.19).
Show that equation (29.10) reduces to (29.4) as the 4, send to zero.
What is the advantage of LMM over BGM?
"When the forward rate volatility a,T) in LMM is constant, the Ho-Lee model results." Verify that this is true by showing that LMM gives a process for bond prices that is consistent with the Ho-Lee
Compare results for the following cases: (a) Option is Europeanc connal model with e-0.01 and a-0.05 (b) Option is European, lognormal model with (c) Option is American; nonnal model with (d) Option
Use the DerivaGems software to value 1x4, 2x3, 3x2, and 4x 1 European swap options to receive floating and pay food. Assume that the 1-, 2-, 3-, 3-, and 5-year Interest rates are 3%, 3.5%, 3.8%,
A trader wishes to compute the price of a 1-year American call option on a 5-year bond with a face value of 100. The bond pays a coupon of 6% semiannually and the (quoted) strike price of the option
What does the calibration of a one-factor term structure model involve? 28.20 Use the DerivaGem software to value 1x4, 2x3, 3x 2, and 4x 1 European wwwp options to receive fixed and pay floating.
18.17. Calculate the price of a 2-year zero-coupon band from the tree in Figure 28.9 and verify that it agrees with the initial term structure.
Use a change of numeraire argument to show that the relationship between the futures rate and forward rate for the Ho-Lee model is as shown in Section 6.4. Use the relationship to verify the
28.11. In the Hell-White model, a 0.08 and 0.01. Calculate the price of a 1-year European call option on a zero-coupon bond that will mature in 5 years when the ten structure is flat at 10%, the
Suppose that a 01, 0008, and 0.015 in Vasicek's model, with the initial value of the short rate being 5% Calculate the price of a 1-year European call option on a zero-coupon bond with a principal of
Can the approach described in Section 28.4 for decomposing an option on a coupon- bearing bond into a portfolio of options on zero-coupon bonds be used in conjunction with a two-factor model? Explain
The payoff from a derivative will occur in 8 years. It will equal the average of the 1-year interest rates observed at times 5, 6, 7, and 8 years applied to a principal of $1,000. The yield curve is
Consider instrument that will pay off S dollars is 2 years, where S is the value of the Nikkel indes. The index is currently 20,000. The yen dollar exchange rate is 100 (yes per dollar). The
A call option provides a payoff at time of max(S-K, 0) yen, where Sy is the dollar price of gold at time 7 and K is the strike price. Assuming that the storage costs of gold are zero and defining
The variables is an investment asset providing income at rate measured in currency A It follows the process d=d+ in the real world. Defining new variables as necessary, give the process followed by
Explain whether any convexity or timing adjustments are necessary when. (a) We wish to value a spread option that pays off every quarter the excess (if any) of the 5-year swap rate over the 3-month
Explain how you would value a derivative that pays off 100 in 5 years, where R is the 1-year interest rate (annually compounded) observed in 4 years. What difference would it make if the payoff were
Use the Deriva Gem software to value a European swap option that gives you the right in 2 years to enter into a 5-year swap in which you pay a fixed rate of 6% and receive floating Cash flows are
Suppose that the LIBOR yield curve is flat at 8% with annual compounding A swaption gives the holder the right to receive 7.6% in a 5-year swap starting in 4 years. Payments are made annually. The
Use DerivaGen to determine the value of an option to pay a fixed rate of 6% and receive LIBOR on a 5-year swap starting in I year. Assume that the principal is $100 million, payments are exchanged
If the yield volatility for a 5-year put option on a bond maturing in 10 years time is specified as 22%, how should the option be valued? Assume that, based on today's interest rates the modified
Calculate the value of a 4-year European call option on bond that will mature 5 years from today using Black's model. The 5-year colt bond price is $105, the cash price of a 4-year bond with the same
Calculate the price of an option that caps the 3-mouth rate, starting in 15 months time, at 13% (quoted with quarterly compounding) on a principal amount of $1,000. The forward interest rate for the
Explain carefully how you would use (a) spoc volatilities and (b) flat volatilities to value 5-year cap. a
25.14. Show that when h/o and and are each dependent on a Wiener processes, the ith component of the volatility of wis the ith component of the volatility of A minus the ith component of the
Prove equation (25.33) in Section
Prove the result in Section 25.5 that when and dg with thed, uncorrelated, //a is a martingale for
Prove that, when the security provides income at rate, equation (259) becomes +. (Mau: Form a new security that provides no income by assuming that all the income from f is reinvested in 75
Suppose that an interest rate x follows the process wherea, x, and care positive constants. Suppose further that the market price of risk for x is. What is the process for x in the traditional
Consider the situation in Merton's jump-diffusion model where the underlying asset is a non-dividend paying stock. The average frequency of jumps is one per year. The average percentage jump size is
Suppose that the volatilities used to price a 6-month currency option are as in Table 16.2 Assume that the domestic and foreign risk-free rates are 5% per annum and the current exchange rate is 1.00.
Write down the equations for simulating the path followed by the asset price in the stochastic volatility model in equations (4.2) and (24.3).
"HDD and CDD can be regarded as payoffs from options on temperature" Explain this statement. 23.& Suppose that you have 50 years of temperature data at your disposal. Explain carefully the analy you
Distinguish between the historical data and the risk-neutral approach to valuing a derivative. Under what circumstance do they give the same answer.
It shows the way a hedge can be constructed using four options (as in Section 22.13) and two ways a hodge can be constructed using 16 options (a) Explain the difference between the two ways a hedge
Estimate the value of a new 6-month European-style average price call option on a non- dividend paying stock. The initial stock price is $30, the strike price is $30, the risk-free interest rate is
Answer the following questions about compound options (a) What put-call parity relationship exists between the price of a European call on a call and a European put on a call? Show that the formulas
How can the value of a forward start pat option on a non-dividend paying stock be calculated if it is agreed that the strike price will be 10% greater than the stock price at the time the option
Suppose that the strike price of an American call option on a non-dividend paying stock grows at rate g. Show that if is less than the risk-free rate, r, it is never optimal to exercise the call
Section 22.6 gives two formulas for a down-and-out call. The first applies to the situation where the barrier, H, is less than or equal to the strike price, K. The second applies to the situation
Consider a chooser option where the holder has the right to choose between a European call and a European pat at any time during a 2-year period. The maturity dates and strike prices for the calls
How does a 5-year eth-to-default credit default swap work? Consider a basket of 100 reference entities where each reference entity has a probability of defaulting in each year of 1%. As the default
What is the credit default swap spread in Problem 21.8 if it is a binary CDS?
Suppose that the risk-free zero curve is dat at 7% per annum with continuous compounding and that defaults can occur halfway through each year in a new 5-year credit default swap. Suppose that the
Suppose that a bank has a total of $10 million of exposures of a certain type. The 1-year probability of default averages 1% and the recovery rate averages 40%. The copsis correlation parameter is
Explain carefully the distinction between real-world and risk-neutral default probabil ities. Which is higher? A bank esters into a credit derivative where it agrees to pay $100 at the end of 1 year
Suppose a 3-year corporate bond provides a coupon of 7% per year payable semianna- ally and has a yield of 5% (expressed with semiannual compounding). The yields for all materities on risk-free bonds
Suppose that in an asset swap is the market price of the bond per dollar of principal, * is the default-free value of the bond per dollar of principal, and V is the present value of the asset swap
"When a bank is negotiating currency swaps, it should try to ensure that it is receiving the lower interest rate currency from a company with a low credit risk." Explain why.
Suppose that in Problem 20.17, the 6-month forward rate is also 1.50 and the 6-month dollar risk-free interest rate is 5% per annum. Suppose further that the 6-month dollar rate of interest at which
A company has issued 3- and 5-year bonds with a coupon of 4% per annum payable annually. The yields on the bonds (expressed with contous compounding) are 4.5% and 4.75%, respectively. Risk-free rates
A 4-year corporate bond provides a coupon of 4% per year payable semiannually and has a yield of 5% expressed with continuous compounding. The risk-free yield curve is Blat at 3% with continuous
Suppose that the probability of company A defaulting during a 2-year period is 0.2 and the probability of company B definiting during this period is 0.15. If the G copula measure of default
Suppose that the measure (7) in equation (20.9) is the same in the real world and the risk-natal world. Is the same true of the Gaussian copula measure, PA
Verify (a) that the numbers in the second column of Table 20.4 are consistent with the numbers in Table 20.1 and (b) that the numbers in the fourth column of Table 20.5 are consistent with the
Explain the difference between an unconditional default probability density and a default intensity
The spread between the yield on a 3-year corporate bond and the yield on a similar risk- free bond is 50 basis points. The recovery rate is 30% Estimate the average default intensity per year over
Suppose that the parameters in a GARCH (1.1) model are a 0.03, 8-0.95, and -0.000002 (a) What is the long-com average volatility? (b) If the current volatility is 1.5% per day, what is your estimate
An Excel spreadsheet containing over 900 days of daily data on a number of different exchange rates and stock indices can be downloaded from the author's website: http://www.rotman.utoronto.ca/-ball
In practice, is the parameter likely to be the same for gold and silver?
Suppose that the price of gold at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility estimate
Show that the GARCH (11) model =+av+ in equation (199) is equivalent to the stochastic volatility model dV-V-V)dt+Vds, where time is measured in days, V is the square of the volatility of the asset

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