Question: Consider the June 165, 170, and 175
Consider the June 165, 170, and 175 call option prices in Table 9.1. 
a. Does convexity hold if you buy a butterfly spread, buying at the ask price and selling at the bid? b. Does convexity hold if you sell a butterfly spread, buying at the ask price and selling at the bid? c. Does convexity hold if you are a market-maker either buying or selling a butterfly, paying the bid and receiving the ask?
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TABLE 9.1 IBM option prices, dollars per share, May 6, 2011. The closing price of IBM on that day was $168.89. Calls Puts Strike Expiration Bid ($) Ask ($) Bid ($) Ask ($) 160 June 10.05 10.15 1.16 1.20 165 June 6.15 6.25 2.26 2.31 170 June 3.20 3.30 4.25 4.35 175 June 1.38 1.43 7.40 7.55 160 October 14.10 14.20 5.70 5.80 165 October 10.85 11.00 7.45 7.60 170 October 8.10 8.20 9.70 9.85 175 October 5.80 5.90 12.40 12.55
> Compute estimated profit in 1 year if XYZ buys collars with the following strikes: a. $0.95 for the put and $1.00 for the call. b. $0.975 for the put and $1.025 for the call. c. $1.05 for the put and $1.05 for the call. Draw a graph of profit in each cas
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> Repeat Problem 17.18 assuming that the volatility of gold is 20% and that once opened, the mine can be costlessly shut down once, and then costlessly reopened once. What is the value of the mine? What are the prices at which the mine will be shut down an
> Firm A has a stock price of $40, and has made an offer for firm B where A promises to pay 1.5 shares for each share of B, as long as A’s stock price remains between $35 and $45. If the price of A is below $35, A will pay $52.50/share, and if the price of
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> The S&R index spot price is 1100, the risk-free rate is 5%, and the continuous dividend yield on the index is 2%. a. Suppose you observe a 6-month forward price of 1120. What arbitrage would you undertake? b. Suppose you observe a 6-month forward price o
> Suppose that S = $50, K = $45, σ = 0.30, r = 0.08, and t = 1. The stock will pay a $4 dividend in exactly 3 months. Compute the price of European and American call options using a four-step binomial tree.
> A DECS contract pays two shares if ST < 27.875, 1.667 shares if the price is above ST > 33.45, and $27.875 and $55.75 otherwise. The quarterly dividend is $0.87. Value this DECS assuming that S = $26.70, σ = 35%, r = 9%, and T = 3.3 and that the underlyi
> Suppose that S = $100, σ = 30%, r = 8%, and δ = 0. Today you buy a contract which, 6 months from today, will give you one 3-month to expiration at-the-money call option. (This is called a forward start option.) Assume that r, σ, and δ are certain not to
> Consider a 5-year equity-linked note that pays one share of XYZ at maturity. The price of XYZ today is $100, and XYZ is expected to pay its annual dividend of $1 at the end of this year, increasing by $0.50 each year. The fifth dividend will be paid the
> Repeat the previous problem, but this time for perpetual options. What do you notice about the prices? What do you notice about the exercise barriers? Previous Problem Let S = $100, K = $90, σ = 30%, r = 8%, δ = 5%, and T = 1. a. What is the Black-Schole
> Suppose the yield curve is flat at 8%. Consider 3- and 6-year zero-coupon bonds. You buy one 3-year bond and sell an appropriate quantity of the 6-year bond to duration hedge the position. Any additional investment is in short-term (zero-duration) bonds.
> In this problem we consider whether parity is violated by any of the option prices in Table 9.1. Suppose that you buy at the ask and sell at the bid, and that your continuously compounded lending rate is 0.3% and your borrowing rate is 0.4%. Ignore tr
> For a stock index, S = $100, σ = 30%, r = 5%, δ = 3%, and T = 3. Let n = 3. a. What is the price of a European call option with a strike of $95? b. What is the price of a European put option with a strike of $95? c. Now let S = $95, K = $100, σ = 30%, r
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> Here is a quote from an investment website about an investment strategy using options: One strategy investors are applying to the XYZ options is using “synthetic stock.”Asynthetic stock is created when an investor simultaneously purchases a call option a
> Let S = $40, σ = 0.30, r = 0.08, T = 1, and δ = 0. Also let Q = $60, σQ= 0.50,δQ= 0, and ρ = 0.5. In this problem we will compute prices of exchange calls with S as the price of the underlying asset and Q as the price of the strike asset. a. Vary δ from
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> Use the same assumptions as in the preceding problem, without the bid-ask spread. Suppose that we want to construct a paylater strategy using a ratio spread. Instead of buying a 440-strike call, Auric will sell one 440-strike call and use the premium to
> Using Monte Carlo, simulate the process dr = a(b − r)dt + σ, assuming that r = 6%, a = 0.2, b = 0.08, φ = 0 and σ = 0.02. Compute the prices of 1-, 2-, and 3-year zero coupon bonds, and verify that your answers match those of the Cox- Ingersoll-Ross for
> Compute estimated profit in 1 year if Telco buys a call option with a strike of $0.95, $1.00, or $1.05. Draw a graph of profit in each case.
> Using the CEV option pricing model, set β = 3 and generate option prices for strikes from 60 to 140, in increments of 5, for times to maturity of 0.25, 0.5, 1.0, and 2.0. Plot the resulting implied volatilities.
> Consider Example 6.1. Suppose the February forward price had been $2.80. What would the arbitrage be? Suppose it had been $2.65. What would the arbitrage be? In each case, specify the transactions and resulting cash flows in both November and February. W
> Repeat Problem 17.18 assuming that the volatility of gold is 20% and that once opened, the mine can be costlessly shut down forever. What is the value of the mine? What is the price at which the mine will be shut down? Repeat Problem 17.18 A mine costin
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> Repeat the previous problem, except that instead of hedging volatility risk, you wish to hedge interest rate risk, i.e., to rho-hedge. In addition to delta-, gamma-, and rho-hedging, can you delta-gamma-rho-vega hedge? Data from Previous Problem You hav
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> Use the same inputs as in the previous problem. Suppose that you observe a bid option price of $50 and an ask price of $50.10. a. Explain why you cannot compute an implied volatility for the bid price. b. Compute an implied volatility for the ask price,
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> Estimate a GARCH (1,1) for the S&P 500 index, using data from January 1999 to December 2003.
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> Construct an asymmetric butterfly using the 950-, 1020-, and 1050-strike options. How many of each option do you hold? Draw a profit diagram for the position.
> Suppose that the exchange rate is 1 dollar for 120 yen. The dollar interest rate is 5% (continuously compounded) and the yen rate is 1% (continuously compounded). Consider an at-the-money American dollar call that is yen-denominated (i.e., the call permi
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> Verify that e−r(T−t)N(d2) satisfies the Black-Scholes equation.
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> An option has a gold futures contract as the underlying asset. The current 1-year gold futures price is $300/oz, the strike price is $290, the risk-free rate is 6%, volatility is 10%, and time to expiration is 1 year. Suppose n = 1. What is the price of
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> What are the two methods that can be used to account for the combination of two or more private not-for-profit entities into a single entity?
> When should membership dues be considered revenue rather than contributions?
> What is the difference between an unconditional promise to give and an intention to give?
> A private not-for-profit entity receives numerous pledges of financial support to be conveyed at various times over the next few years. Under what condition should these pledges be recognized as receivables and contributed support? At what amount should
> A private not-for-profit entity sends a direct mail solicitation for monetary donations. Other information is included with the mailing. Under what conditions can the organization report part of the cost of this mailing as a program service cost rather t
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> Under what conditions does a not-for-profit entity record donated services?
> What is a debtor in possession? a. The holder of a note receivable issued by an insolvent company prior to the granting of an order for relief. b. A fully secured creditor. c. The ownership of an insolvent company that continues to control the organizati
> Through the payment of $10,468,000 in cash, Drexel Company acquires voting control over Young Company. This price is paid for 60 percent of the subsidiary’s 100,000 outstanding common shares ($40 par value) as well as all 10,000 shares of 8 percent, cumu
> Arcola, Inc., acquires all 40,000 shares of Tuscola Company for $725,000. A year later, when Arcola’s equity adjusted balance in its investment in Tuscola equals $800,000, Tuscola issues an additional 10,000 shares to outside investors for $25 per share.
> A donor gives a gift to a charity that is to be conveyed to a separate beneficiary. What is the method of reporting for each party if the charity receives variance power enabling it to change the identity of the beneficiary?
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> Read several of the following articles as well as any other published pieces that describe the work of the accountant in bankruptcy cases: “Restructuring for a Positive Return,” CMA Management, December 2005/January 2006. “Alternatives to Bankruptcy Liqu
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