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Derivatives (3) Currency Options: Basics

Derivatives (3) Currency Options: Basics. Dr. J.D. Han King’s College, UWO. 1.History of (FX) Options. Notion dates to ancient times Secondary Market for Options were developed by Chicago Board of Trade in 1973

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Derivatives (3) Currency Options: Basics

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  1. Derivatives (3)Currency Options: Basics Dr. J.D. Han King’s College, UWO

  2. 1.History of (FX) Options • Notion dates to ancient times • Secondary Market for Options were developed by Chicago Board of Trade in 1973 • Options on FX(Currencies) were developed by Philadelphia Stock Exchange PHLX in 1983, and are successful. • CBOT introduced FX Options with less success. • As of F1 2009, NASDAQ has acquired and absorbed PHLX. http://www.usatoday.com/money/markets/2007-11-07-nasdaq-philadelphia-exchange_N.htm - • A New PHLX ‘Word Currency Option’ is created at the NASDAQ.

  3. 2. Underlying Assets • Equities - Stock • Equity indices • Interest rates - various maturities • Foreign Exchanges=FX • Commodities

  4. 3. Food for Thought: Option and Lottery Ticket Why is “lottery” so attractive and popular? Lottery tickets do not cost very much. In the worst case, the buyer loses the small sum. In the best case, he may hit a big money. Lottery has ‘asymmetrical’ position with respect to downside risk and upside potential. The same is true with financial options.

  5. 4. Characteristics of Options • Right versus Obligation • Option contracts convey a right without an obligation to buyer (owner) -> A buyer has a right to buy, or a right to sell an “underlying” asset at the agreed price. • Option contracts impose an obligation on seller (writer) ->A seller has an obligation to sell, or an obligation to buy an “underlying” asset at the agreed price.

  6. 2) Buyer versus Seller The Option buyer are ‘owners’, and are said to be “long” with option However they could be selling(short) or buying(long) the underlying products/instruments Option buyers may buy “right” to buy at Strike Price– call option Or may buy “right” to sell at Strike Price– put option Option sellers are ‘writers’, and are said to be “short”

  7. Why do you pay premium? Because You want to have the right only and to get exempted from obligation. • What does this mean for your Payoff curve? Downside risks are eliminated.

  8. In other words, You turn Forward into Option by paying premium. You eliminate the Downside Risk and have only the Upside Potentials.

  9. A ‘Hedger’ of FX market will be rarely selling any option unless he thinks it is impossible to have the situation where the Option is to be exercised at all. • But sometime he thinks and that is when he makes a mistake……

  10. What do you buy? You may buy “right” to take a long-position, or to buy FX at Strike Price– you may buy call option Or may buy “right” to sell at Strike Price– you may buy put option Which one choose? With long call option, you will make profits if spot price St+1 goes up but still you can buy at a lower strike price If spot price falls, you just give up the premium and do not exercise option. You will not loose much.

  11. It could be confusing as there are two levels of buying and selling: Buying or selling option, and buying or selling underlying products/instruments/assets. • Long position(to benefit from a rising Et+1) is now to be associated with the Call; Short position(to benefit from a falling Et+1) with the Put. • And, as a hedger, you will buy Call Option or Put Option, and will never sell a single vanilla option*. *As a hedger, you may be able to sell synthetic options without incurring/taking any risks.

  12. 3) Call versus Put • Call Options : A Call Option buyer buys/has a right to buy products/instruments at pre-set price: ->He will win if the price of the underlying products/asset goes up. Put Options : The Put Option buyer has/buys a right to sell products/instruments at the ‘strike price’. ->He will win if the underlying product/asset price falls.

  13. What creates this ‘asymmetrical position’ between a buyer and a seller? • It is the ‘Premium’ of an option- the deposit that the buyer pays to the seller. • Because of the premium received, the seller now has an obligation, but not a right.

  14. 4) Premium= Option Pricing • The premium is the price paid by Buyer to Seller to acquire an option contract • Premium size indicates how valuable the option is considered • There are many option pricing models, and Black and Scholes’ model is best known. • Garman-Kohhagen have modified B-S model of Option pricing for the FOREX market.

  15. *Garman-Kohlhagen Model of FX currency Options • Mathematical Model • Excel Calculator Click here for an Excel Calculator for Option Premium There are two kinds of Options in terms of Pricing: -”In the money option”: Potentially, you can make profits by exercising it. <- E or Et+1 > X for call options <- E or Et+1< X for put options -” Out of the money option”:

  16. 5) Exercise Features • Exercising an option is done by the owner in accordance with its provisions • American options can be exercised at any time before expiration • European options can be exercised only on their expiration date • Exercise is accomplished at the agreed ‘exercise’ or ‘strike’ price (X)

  17. How do you make a profit from the option contract? • If you are a buyer of a FX call option, you have a right to buy the FX at the strike price(rate). • You wait until the expiration date, and compare the strike price(rate) X from the previous period and the current actual spot rate Et+1: - If X< Et+1, you exercise the option contract and buy the FX at X. - If X>Et+1, you can buy the FX cheaper at the spot market than through the option contract. You just do NOT exercise your right for the option, and walk out.

  18. *Exercise Question. If you expect the price of an asset to go down in the, what option would you buy? (circle for the answer) You are buying (call/put) option of the asset at the pre-set strike price which should be (higher/lower) than your expected lowest future price: You pay the premium to the other party. You become the option owner and the other party becomes the option writer who gets the premium. Now you have only the right to (buy/sell), and the option writer has only the obligation to accommodate you. Your gains will be his loss, vice versa. You will wait the spot price of the asset to (rise/fall) (above/below) the pre-set strike price. When the spot price goes (above/below) the pre-set strike price as you have expected, you will exercise the option to (buy/sell) the currency (from/to) the option writer, and (buy/sell) the asset at the spot market. You may make profits. If the spot price does not go (above/below) the pre-set price, you will simply let the deal expire. All you have lost is the premium.

  19. Note that Options are symmetrical: Pay-offs of Put (sell underlying assets)Call (buy underlying assets) Long with Option: buying the right to be Having right to sell at X however low Et+1 goes, Having right to buy at X however high Et+1 goes up Short with Option: Selling/accepting the obligation to be Having obligation to buy at X however low Et+1 goes. Having obligation to sell at X however high Et+1 goes Vertically, the sum of gains and loss of the two partners = 0; Zero Sum Game like any other financial games

  20. Note that Options are symmetrical: Pay-offs of Put (Sell/Short underlying assets)Call (Buy/Long underlying assets) Long with Option: buying the right to be Short with Option: Selling/accepting the obligation to be

  21. Note that • For the hedger. • Forward Long (hedging) is closely related to Long Call Option (to protect against a rising Et+1) • Forward Short(hedging) is closely related to Long Put Option (to protect against a falling Et+1) • For a single option, a hedger will buy an option, and will NOT sell a single option.

  22. 5. Illustration • Symbols employed Et (or e) = current spot FOREX rate Et+1 = future spot FOREX rate X = Exercise price (Contracted Price; Pre-set Price; similar to “F” in forward contract) C = Call premium P = Put premium T = Time until option expires

  23. 2) Net Pay-off = - Premium (You pay at the beginning) + Gross Pay-off (your profit/Loss at t+1 by comparing X(determined; fixed) and Et+1(stochastic; to be realized)

  24. Example 1: ‘Long Call’ • You pay some premium, and buy the right to buy goods/products/instruments/assets at the pre-set price of X.

  25. Step 1. Premium paid Zero Pay-off line Et+1 Premium Paid When you are buying an option, you pay Premium That gives you a right (to buy or to sell at the agreed price) and no obligation.

  26. Step 2: Gross Pay-off: your profit/loss at t+1 before you pay the Premium Gross Pay-off Constraint: Call Option Pay-off =max ( 0 ; St+1 – X ) If St+1<F, you just do not exercise the right to buy at X. No loss/gain. If St+1>F, you exercise the right to buy at X low from option contract, and sell at St+1 high on spot market. You make profits of S t+1 – X;

  27. Step 3: Net Pay-off: After paying the Premium Net Payoff (Payoff - Cost) : Combining the previous 2 graphs and read vertically (with the horizontal line of Et+1 being the zero profit line). X 0(zero) Break-even point Note: 1)At X, the pay off curve turns; 2) To have a break-even and more, Et+1 should be at, or higher than, X by the premium paid (CFA exam).

  28. Note that Options are symmetrical: Pay-offs of Put (Sell/Short underlying assets)Call (Buy/Long underlying assets) Long with Option: buying the right to be Short with Option: Selling/accepting the obligation to be

  29. Once you have got the payoff line of Long Call, you can get the payoff line of Short Call because The sum of payoffs of Long Call and Short Call is always equal to zero: Zero Sum Game.

  30. Example 3: Long Put • You are buying a Put Option by paying the premium. You are buying the right to sell at X. Step 1: Paying the premium by this much

  31. Step 2: Gross Pay-off of Put Option X Et+1 Your gross profit= max { X-Et+1, 0} If Et+1 turns out to be lower than X, as you exercise the right to sell the products/assets at X that you may buy at Et+1 the spot market. You may profit of X - Et+1 If Et+1 turns out to be higher than X, you do not have an obligation to sell through option contract. You may just walk out. The loss is nil or zero.

  32. Step 3: Combining the two graphs to get the Net Pay-off

  33. Again you can get the Payoff of Short Put Option from the above: They are the opposite of each other because the sum of two payoffs (buyer and seller of the Put Option here is equal to zero at all times.

  34. Example 4: Short Putyou can get this from Example 3 by invoking the Zero Sum Game principle. X

  35. 6. Why Using Options? 1) Hedging, but Nicer than Forward/Future: Suppose that you are a Canadian exporter with the receivable of US $1 million and your receivable is subject to FOREX risks. However, you do not like the forward hedging which eliminates upside potential as well as downside risk. What would be your hedging which preserves the upside potential? 2) Overcoming lack of Liquidity: Suppose that the forward FOREX market is not liquid, and thus you cannot get “short” forward with US dollars. Now you can make it up or synthesize it by combining a few options. In fact, the “synthetic” option may be cheaper with a lower net premium. Here, the hedger may even sell Option(s) in his multiple option transactions. How? We will look into “Synthetic Options”.

  36. 7. World Currency Option Trade • This example assumes that the Euro spot rate is at US $ 1.2806 at the time of the trade, say, March. • You believe that the FX rate will rise for Euro in the future, say, October. You go for Long Call of Euro.Suppose that you manage to get the Strike Price of 128.0 as follows: A Euro call is expressed as 128.0 - (the same as with index options, by the custom, the FX option market moves the decimal point two places to the right).Premium is quoted in cents for a unit of FX: An investor buys one October 128.0 Euro call for, say, 1.15. The premium (bids and offers) is made in terms of U.S. dollars per unit of FX. One unit of the contract size is 10,000 Euros. Thus, the total premium is 1.15 U.S. cents times 10,000 = 115 U.S. dollars. In a quick way, the premium is calculated with a $100 multiplier: the premium of 1.15 (quoted premium) times 100, which will be in dollar terms. In this case, it costs US $115.00.The option here is only European one. Thus you wait until October. Suppose that the Euro rises to U.S. $ 1.3300 at option expiration date, that is, October, the net value of this call option would be equal to the net profit you can make by exercising the option: In this case, you may buy Euro 10,000 for U.S. $ 12,800 by excercising the option contract and sell them at the spot market at U.S. $13,300 . This is because the option price at the expiration date is equal to the spot price. The call could be sold to close the position or be exercised.The proceeds would be:Gross Proceeds from sale: $500Premium or Cost of the Option: $115Net Profit: $385 • This is the intrinsic value, and there is no time value as it is to expire.

  37. PHLX FX Options http://www.nasdaq.com/includes/currency-help-faqs.stm • Contract size 10,000 units of FX (except for 1,000,000 of Japanese Yen) • Premium/Price quoted in U.S. cents for every unit of FX Thus the price of each contact is whatever cents times 10,000.

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