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The Department of Finance
Introductory Options Markets
Midterm Examination, Spring Semester 2009
Note:
l Answer the problems in order of appearance.
l This is a take home exam, and the paper is due at 09:00 a.m. on April 20, 2009.
l Discussion of the exam materials with anyone else is strictly prohibited.
Problems/Questions:
1. (50 points, 5 points for each part) Find the closing prices of Taiwan Composite Index Options (TXO) on April 13, 2009, and answer the following questions. Your answers to some of the questions may refer to the closing index points on the same day.
(1) Briefly describe the major terms of the index options, including the underlying asset, the type of options, the trading hours, the contract multiplier, the settlement, and the determination of final settlement price.
(2) Compute the time values and intrinsic values for five May calls and five May puts with strikes surrounding the closing index points. Discuss the pattern of time values.
(3) Discuss the effects of major determinants on option prices. Specifically, how and why does the price of underlying asset affect option prices? The effect of riskless interest rates?
(4) Continue from part #1-3. Time to expiration? Stock return volatility?
(5) Which strategy is more risky? Buying a May 5500 call versus buying a May 5900 call. Explain.
(6) Suppose you are mildly bullish about the index movement until mid-May. What strategy should you use to maximize your profit from your market view? Explain carefully.
(7) Suppose you bought a basket of stocks for \$10 million at the index level of 5500. Given the current index level, how many TXO put options do you need to lock in your profit. Which put option should you use? Explain.
(8) Compute the price you should pay for buying a May 5700 straddle. Suppose the index ends up in the range of (5200, 6200), show the Profit/Loss diagram in terms of dollars and percentages.
(9) Compute the margin deposit needed for selling short ten (10) May 5700 puts. When does this strategy make sense? What is the risk associated with this strategy? What is the maximum return?
(10) Compute the margin deposit needed for selling short one (1) May 5500/5900 strangle. When does this strategy make sense? What is the risk associated with this strategy? What is the maximum return?
 Call Strike Price Put May June May June
2. (20 points, 5 points for each part) Properties of stock option prices.
(1) Explain why an American option is always worth at least as much as its intrinsic value.
(2) Explain why a zero-strike call option is worth the value of a stock.
(3) Explain why a European put option could have a negative time value, while an American put option could not.
(4) Compute the cash flow of buying one May 5500 call, selling two May 5700 calls, and buying one May 5900 calls. Why should the value of buying a butterfly spread be positive? Explain.
3. (20 points, 7 points for each part) Binomial option pricing model. Suppose the stock price is now \$40, the strike price is \$40, the volatility of stock return is 20%, and the riskless interest rate is 5%.
(1) Compute the price of a 6-month European call option on a non-dividend paying common stock. Be sure to check the convergence criterion.
(2) For the option in part #3-1, construct its Delta-tree and Bond-Face-tree if the expiration is divided into 5 periods. Use this structure to illustrate with an example the process of “dynamic replication of option’s terminal payoff”.
(3) Do part #3-2 again for a 6-month American PUT option.
4. (20 points, 7 points for each part) On the dynamic hedging strategy. Suppose you issue 1,000 units of call warrants on XYZ common shares. The stock price is now \$50. The call is worth \$10, the delta is 0.50, gamma is 0.05, theta is 10.0, and vega is 5.0. Answer the following.
(1) Comment on the following statement. “The concept of zero-sum game of derivatives markets implies: The writers of call options make money when the buyers lose. Therefore, when securities houses issue call warrants on stock XYZ, the market outlook for XYZ is pessimistic.”
(2) Compute the delta-neutral hedging position for the warrants. Compute the approximate hedging costs if you follow a delta-neutral strategy and the stock price changes instantly by ±\$1.0 and ±\$3.0, respectively.
(3) Do part #4-2 again except that you over-hedge by using a delta of 0.6, instead.
5. (20 points, 7 points for each part) On warrant issuance business.
(1) Describe the nature of warrant issuing business from the point of view of a securities house. How do they make a profit from such business?
(2) There are usually several call warrants on the same underlying stocks in the listed warrant market. When making a choice among similar warrants on TSMC (ticker number: 2330.tw), what information is more relevant for warrant investors?
(3) If you were to issue warrants, how would you pick your underlying? How to price the warrants? What risks do you face and what could you do to manage the risks? Discuss concisely.
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• 2009-04-14 19:28
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