Options on Stock Indices, Currencies, and Futures Chapter 13

1. Options onStock Indices, Currencies, and FuturesChapter 13

2. STOCK INDEX OPTIONS ONE CONTRACT VALUE = (INDEX VALUE)($MULTIPLIER) One contract = (I)($m) ACCOUNTS ARE SETTLED BY CASH

3. STOCK INDEX OPTIONS FOR • PORTFOLIO INSURANCE • Problems: • How many puts to buy? • Which exercise price will guarantee the desired level of protection? • The answers are not easy because the • index underlying the puts is not the • portfolio to be protected.

4. The protective put with a single stock:

5. The protective put consists of holding the portfolio and purchasing n puts.

6. WE USE THE CAPITAL ASSET PRICING MODEL. For any security i,the expected excess return on the security and the expected excess return on the market portfolio are linearly related by their beta:

7. THE INDEX TO BE USED IN THE STRATEGY, IS TAKEN TO BE A PROXY FOR THE MARKET PORTFOLIO, M. FIRST, REWRITE THE ABOVE EQUATION FOR THE INDEX I AND ANY PORTFOLIO P :

8. Second, rewrite the CAPM result, with actual returns: In a more refined way, using V and I for the portfolio and index market values, respectively:

9. NEXT, use the ratio Dp/V0 as the portfolio’s annual dividend payout ratio qP and DI/I0 the index annual dividend payout ratio, qI. The ratio V1/ V0 indicates the portfolio required protection ratio.

10. For example: The manager wants V1, to be down to no more than 90% of the initial portfolio market value, V0: V1 = V0(.9). We denote this desired level by (V1/ V0)*. This is the decision variable.

11. 1. The number of puts is:

12. 2.The exercise price, K, is determined by substituting I1 = K and the required level, (V1/ V0)* into the equation: and solving for K:

13. We rewrite the Profit/Loss table for the protective put strategy: We are now ready to calculate the floor level of the portfolio: V1+n($m)(K- I1)

14. We are now ready to calculate the floor level of the portfolio: Min portfolio value = V1+n($m)(K- I1) This is the lowest level that the portfolio value can attain. If the index falls below the exercise price and the portfolio value declines too, the protective puts will be exercised and the money gained may be invested in the portfolio and bring it to the value of: V1+n($m)K- n($m)I1

15. Substitute for n:

16. To substitute for V1we solve the equation:

17. 3. Substitution V1 into the equation for the Min portfolio value The desired level of protection is made at time 0. This determines the exercise price and management can also calculate the minimum portfolio value.

18. EXAMPLE: A portfolio manager expects the market to fall by 25% in the next six months. The current portfolio value is $25M. The manager decides on a 90% hedge by purchasing 6-month puts on the S&P500 index. The portfolio’s beta with the S&P500 index is 2.4. The S&P500index stands at a level of 1,250 points and its dollar multiplier is $100. The annual risk-free rate is 10%, while the portfolio and the index annual dividend payout ratios are 5% and 6%, respectively. The data is summarized below:

19. Solution: Purchase

20. The exercise price of the puts is: Solution: Purchase n = 480 six-months puts with exercise price K = 1,210.

22. CONCLUSION: Holding the portfolio and purchasing 480, 6-months protective puts on the S&P500 index, with the exercise price K = 1210, guarantees that the portfolio value, currently $25M, will not fall below $22,505,000 in six months.

23. Example (page 274) protection for 3 months Solution: Purchase

24. The exercise price of the puts is: Solution: Purchase n = 10 six-months puts with exercise price K = 960.

26. CONCLUSION: Holding the portfolio and purchasing 10, 3-months protective puts on the S&P500 index, with the exercise price K = 960, guarantees that the portfolio value, currently $500,000 will not fall below $450,000 in three months.

27. A SPECIAL CASE: In the case that • β = 1 and 2. qP =qI, the portfolio is • statistically similar to the index. • In this case:

28. Assume that in the above example, βp = 1 and qP =qI, then:

29. Example: (page 273) βp = 1 and qP =qI, then:

30. FOREIGN CURRENCY FUTURES Standardized Options Currencies Traded: The PHLX lists six dollar-based standardized currency option contracts, which settle in the actual physical currency. These are the most heavily traded currencies in the global inter bank market. Contract Size: The amounts of currency controlled by the various currency options contracts are geared to the needs of the widest possible range of participants.

31. Currency optionsUnits USD/AUD 50,000AUD USD/GBP 31,250GBP USD/CD 50,000CD USD/EUR 62,500EUR USD/JPY 6,250,000JPY USD/CHF 62,500CHF Exercise Style: American- or European options available for physically settled contracts; Long-term options are European-style only.

32. Expiration/Last Trading DayThe PHLX offers a variety of expirations in its physically settled currency options contracts, including Mid-month, Month-end and Long-term expirations. Expiration, which is also the last day of trading, occurs on both a quarterly and consecutive monthly cycle. That is, currency options are available for trading with fixed quarterly months of March, June, September and December and two additional near-term months. For example, after December expiration, trading is available in options which expire in January, February, March, June, September, and December. Month-end option expirations are available in the three nearest months.

33. With the Canadian dollar spot price currently at a level of USD.6556/CD, strike prices would be listed in half-cent intervals ranging from 60 to 70. i.e., 60, 60.5, 61, …, 69, 69.5, 70. If the Canadian dollar spot rate should move to say USD.7060/CD, additional strikes would be listed. E.G, 70, 70.5, 71, …, 75. Standardized Options Exercise PricesExercise prices are expressed in terms of U.S. cents per unit of foreign currency. Thus, a call option on EUR with an exercise price of 82 would give the option buyer the right to buy Euros at 82 cents per EUR.

34. It is important that available exercise prices relate closely to prevailing currency values. Therefore, exercise prices are set at certain intervals surrounding the current spot or market price for a particular currency. When significant price changes take place, additional options with new exercise prices are listed and commence trading. Strike price intervals vary for the different expiration time frames. They are narrower for the near-term and wider for the long-term options.

35. Premium Quotationpremiums for dollar-based options are quoted in U.S. cents per unit of the underlying currency with the exception of Japanese yen which are quoted in hundredths of a cent. Example: A premium of 1.00 for a given EUR option is one cent (USD.01) per EUR. Since each option is for 62,500 EURs, the total option premium would be [62,500DM][USD.01/EUR] = USD625.

36. Customized Currency Options Currencies Traded Customized currency options can be traded on any combination of the currencies currently available for trading. Currently, AUD must be denominated in U.S. dollars. AUD premiums must be denominated in USD. In the case of an option on the USD in CD, the underlying currency is U.S. dollars. The strike prices and premiums are quoted in Canadian dollars. E.G, a call option on the USD with a strike price of 1.542 gives the buyer the right to purchase 50,000 USD at CD1.542/USD.

37. Underlying CurrencyThe underlying currency is that currency which is purchased (in the case of a call) or sold (in the case of a put) upon exercise of the contract. Base CurrencyThe base currency is that currency in which terms the underlying is being quoted, i.e. strike price. Expiration/Last Trading DayExpirations can be established for any business day up to two years from the trade date. Customized option contracts expire at 10:15 a.m., Eastern Time on the expiration day in contrast with standardized options which expire at 11:59 p.m., Eastern Time on the expiration day.

38. In addition, the exercise and assignment process for customized options is more akin to the OTC market in terms of expiration timeframe. Unlike the process utilized for standardized options, exercise notices must be received by 10:00 a.m., Eastern Time and the writer is then notified of the number of contracts assigned. If necessary, contact the PHLX for more details. The contract size for customized currency options is:

39. Underlying currencyContract size Australian dollar 50,000AUD British Pound 31,250GBP Canadian dollar 50,000CD Euro 62,500EUR Japanese Yen 6,250,000JPY Mexican Peso 250,000MXP Spanish Peseta 5,000,000ESP Swiss Frank 62,500CHF USD 50,000USD.

40. Exercise PricesExercise or strike prices may be expressed in any increment out to four characters. For example, a USD/GBP option could have an exercise price of 1.543. Exercise-style European-style only. Minimum Transaction SizeSince customized currency options were designed for the institutional market, there is a minimum opening transaction size which equals or exceeds 50 contracts.

41. A call option on the EUR quoted in American terms would have a strike price expressed in USD. For example, USD.8484 per EUR. A similar option expressed in European terms would be a put option on USD with a strike price expressed in EUR. For example, 1.1787 EUR per USD.

42. Contract TermsAn option may be expressed in either American terms or European terms (inverse terms). For example, an option in American terms would have exercise prices quoted in terms of U.S. dollar per unit of foreign currency. An option in European or inverse terms would have exercise prices quoted in terms of units of foreign currency per U.S. dollar.

43. Trading ProcessTrading is conducted in an open outcry auction market, just as in standardized option contracts. When initial interest in a customized option series is expressed, a floor member must first present a Request For Quote (RFQ) to an Exchange staff member for dissemination. Subsequently, responsive quotes are generated by competing market makers and floor brokers representing off floor interest.

44. PremiumsPremiums may be expressed either in terms of the base currency per unit of the underlying currency or in percent of the underlying currency (based on contract size). For example, the premium for an option on the USD/EUR (USD being the base currency and EURO being the underlying currency) could be expressed in U.S. cents per EUR or as a percentage of 62,500 EUROS.

45. Price and Quote DisseminationRequest For Quotes (RFQs), responsive quotes and trades will be disseminated to the Option Price Reporting Authority (OPRA) for availability to quote vendors The premium for an option on the EUR with a strike price in USD (EUR is the underlying currency and the USD is the base currency) quoted in cents per EUR(premium of 2.50) would be calculated as follows: the aggregate premium for each contract = USD1562.50(USD.025 x 62,500EUR per contract ).Similarly, if this option were quoted in percentage of underlying and the premium was 2.5%, the premium amount for each contract = 1562.5 EUR (.025 x 62,500 EUR per contract).

46. Position LimitsPosition limits are the maximum number of contracts in an underlying currency which can be controlled by a single entity or individual. Currently, position limits are set at 200,000 contracts on each side of the market (long calls and short puts or short calls and long puts) for each currency except the Mexican peso, and the Spanish peseta which are 100,000 contracts. For purposes of computing position limits, all options involving the U.S. dollar against another currency will be aggregated with each other for each currency (i.e., USD/EUR and EUR/USD on the same side of the market will be aggregated - USD/EUR long calls and short puts with EUR/USD short calls and long puts).

47. FX Options As InsuranceOptions on spot represent insurance bought or written on the spot rate. (options on futures represent insurance bought or written on the futures price.) An individual with foreign currency to sell can use put options on spot to establish a floor price on the domestic currency value of the foreign currency. For example, a put option on EUR with an exercise price of USD.80/EUR ensures that, if the value of the EUR falls below USD.80/EUR, the EUR can be sold for USD.80/EUR.

48. If the put option costs USD.01/EUR, the floor price can be roughly approximated as: USD.80/EUR - USD.O1/EUR = USD.79/EUR. That is, if the option is used, the put holder will be able to sell the EUR for the USD.80/EUR strike price, but in the meantime, have paid a premium of USD.01/EUR. Deducting the cost of the premium leaves USD.79/EUR as the floor price established by the purchase of the put. This calculation ignores fees and interest rate adjustments.

49. Similarly, an individual who has to buy foreign currency at some point in the future can use call options on spot to establish a ceiling price on the domestic currency amount that will have to be paid to purchase the foreign exchange.

50. For example, a call option on EUR with an exercise price of USD.80/EUR will ensure that, in the event the value of the EURO rises above USD.80/EUR, the EUR can be bought for USD.80/EUR anyway. If the call option costs USD.02/EUR, this ceiling price can be approximated: USD.80/EUR + USD.02/EUR = USD.82/EUR or the strike price plus the premium.