INTRODUCTION TO OPTIONS MARKETS QUESTIONS

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1 INTRODUCTION TO OPTIONS MARKETS QUESTIONS 1. What is the difference between a put option and a call option? 2. What is the difference between an American option and a European option? 3. Why does an option writer need to post margin? 4. Identify two important ways in which an exchange-traded option differs from a typical overthe-counter option. 5. "There's no real difference between options and futures. Both are hedging tools, and both are derivative products. It's just that with options you have to pay an option premium, while futures require no upfront payment except for a 'good faith margin. I can t understand why anyone would use options." Do you agree with this statement? 6. Explain how this statement can be true: "A long call position offers potentially unlimited gains if the underlying asset s price rises, but a fixed, maximum loss if the underlying asset s price drops to zero." 7. Suppose a call option on a stock has a strike price of $70 and a cost of $2, and suppose you buy the call. Identify the profit to your investment, at the call's expiration, for each of these values of the underlying stock: $25, $70, $100, $ Consider the situation in the previous question once more. Suppose you had sold the call option. What would your profit be at expiration for each of those stock prices? 9. Explain why you agree or disagree with this statement: "Buying a put is just like short selling the underlying asset. You gain the same thing from either position if the underlying asset s price falls. If the price goes up, you have the same loss." 10. You just opened the morning newspaper to check the prices of call options on Asset ABC. It is now December, with the near contract maturing in 1 months time. Asset ABC is currently trading at $50. Strike Jan. March June $40 $11 $12 $ Glancing at the figures, you note that two of these quotes seem to violate some of the rules you learned regarding option pricing. a. What are these discrepancies? b. How could you take advantage of the discrepancies? What is the minimum profit you 1

2 would realize by arbitraging based on these discrepancies? c. Suppose the price of the January $40 call were $9 rather than $11. The option would thus be selling for less than its intrinsic value. Why might it not be the case that an arbitrage profit is instantly available? 12. Indicate whether you agree or disagree with the following statements. a. To determine the theoretical value of an option, we need some measure of the volatility of the underlying asset. Because financial theorists tell us that the appropriate measure of risk is beta (i.e., systematic risk), then we should use this value." b. "It does not make sense that the price of a call option should rise in value if the price of the underlying asset falls." 13. For an asset that does not make cash distributions over the life of an option, it does not pay to exercise a call option prior to the expiration date. Why? INTRODUCTION TO OPTIONS MARKETS ANSWERS TO QUESTIONS 1. A put option is the right to sell a security at a specified price within a specified period of time ("put it to the other party"). A call option is the right to buy a security at a specified price within a specified period of time. 2. An American option can be exercised at any time up until the date of expiration. A European option can only be exercised at time of expiration. 3. An option writer (seller) has agreed to take on all of the risk that the buyer may exercise his option when the price of the underlying asset changes in a direction favorable to the buyer. By definition, one direction of price movement will be unfavorable to the seller. Posting margin protects the clearinghouse and helps guarantee that the seller performs as required. 4. Exchange-traded options are standardized in terms of exercise prices, the size of contracts, and expiration dates. Such standardization is necessary to ensure enough that there are high levels of participation in each contract. It helps the clearinghouse provide liquidity to the market. In addition, standard contracts reduce the transactions costs to participants. 5. The quote fails to recognize that options and futures have fundamental differences. Futures are obligations, whereas buying options gives one the right to perform, but not the obligation. Consequently, they have very different hedging outcomes: futures can be used to lock in a price without the hedger being able to take advantage of a favorable price movement, but an option establishes (based on the strike price) a price for the asset to be hedged but allows the hedger to benefit from a favorable price movement. The more favorable outcome in the case of an option is not free. The cost is the option price or option premium. There is no premium paid in the futures 2

3 market; each side of the transaction is required to perform instead. Futures and exchange traded options may have different underlying assets, which may influence the selection of one or the other for risk management and hedging purposes. 6. As long as the price of the underlying asset increases, the profits increase monotonically. His maximum loss is the price of the option, or the option premium. 7. At an underlying price of $25 the option will not be exercised, and the buyer will lose $2. At $70 there is still no profit in exercising; the loss will still be $2. At $100, the option will be exercised, and the profit will be $100 $70 $2 = $28. At $400, the option will be exercised (enthusiastically), and the profit will be $400 $70 $2 = $ Assuming no transaction cost, an option transaction is a zero sum transaction, meaning that one party s loss is the other s gain. Therefore, the writer s profit or loss would be the mirror opposite of the holder s. In this case, the profit and loss for each situation would be: $2, $2, and $ Disagree. For both a short sale and a long put, an investor profits if the price of the underlying stock falls. But a short sale exposes one to potentially infinite losses as the price of the stock may potentially increase infinitely. In other words, there is no cap to potential losses. A long position in a put option exposes one to losses up to the amount of the option premium. 10. a. The two discrepancies are: (i) the June 40 call is selling for less than the March 40 call despite the fact that the former has a longer time to expiration, and (ii) the June 50 call is trading at a price that is less than the June 60 call, despite the fact that the former has a lower strike price. b. To see how to exploit the second of the two discrepancies, suppose that you buy the June 50 call and sell the June 60 call. The net premium received is $0.50 ($9.00 minus $8.50). Consider what happens under the following scenarios for the price of Asset ABC at the expiration date: if the price is $50 or less, then both calls expire worthless and you get to keep the $0.50 difference in the premiums if the price is above $50 but less than or equal to $60, then the option sold expires worthless and the option purchased will have an intrinsic value equal to the price of Asset ABC at expiration plus $0.50 (the net premium received). Thus, the maximum profit is $10.50 when the price of asset ABC at expiration is $60. if the price is above $60, then the maximum price that can be received for Asset ABC is $60 since the asset will be called at that price by the buyer of the June 60 call. Thus, the profit under this scenario is $

4 To summarize: the profit from exploiting the second premium discrepancy will be between $0.50 and $ As for the first discrepancy, the strategy to exploit it would be to buy the June 40 call at $11.50 and sell the March 40 call at $12. As a result, there would be a net premium received of $0.50. Consider the following scenario for the price of Asset ABC at the expiration of the March contract: if the option is out-of-the-money (if the price of ABC is less than $40), the March call expires worthless but the June 40 call will have some intrinsic value. The gain would be $0.50 plus the market price of the June 40 call. if the option expires in-the-money (if the price of ABC is greater than $40), the intrinsic value of the March 40 call will be equal to the intrinsic value of the June 40 but the latter will have time value. So, as in the previous scenario, the gain is $0.50 plus the time value. c. This would be because of non-synchronous information the closing prices of the stock and options markets are usually taken at different times in the trading day. This is important to emphasize to students. We often find students who have scanned a daily periodical and reported what they believed to be mispricing. Traders use real time quotes to try to uncover mispriced options. 11. a. The payoff is shown below: Spot price + Long Call + Short put = Payoff This payoff structure is equivalent to the forward contract payoffs listed in the text of the question. b. This is because a forward contract requires no initial investment. Thus to replicate the payoff of a forward contract you would find call and put options at the same strike price and the same option price in order to satisfy the condition that no initial investment be made. Buying a call and selling a put at the same option prices would require no investment. 12. a. Disagree. The problem with using the capital asset pricing model and the discounted cash flow method of valuation is that the risks associated with an option changes continuously. Thus, option valuation instead uses the continuous hedging by holding the underlying assets and borrowing funds as a synthetic substitute for the cash flow of an option. b. Disagree. All other factors unchanged, the price of a call option will decline if the asset's 4

5 price declines. However, if another factor that affects the option price changes such that it offsets the adverse affect of a decline in the asset's price, the price of a call can rise. For example, if expected volatility rises, the call option premium can rise. 13. If an option is exercised prior to the expiration date, the intrinsic value will be realized. If, instead, a call option is sold prior to the expiration date, the option premium or value will be realized. The option price includes the intrinsic value and time premium. Thus, early exercise results in the loss of the time premium. Warn students that this is because we assumed that there is no cash distribution that will be realized from holding the asset. If there are cash distributions, then one must evaluate whether the value of the cash distributions (plus any income that can be realized from reinvesting those distributions until the expiration date) exceeds the lost time premium. 5

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