FX Options(I): Basics Dr. J.D. Han King’s College, UWO 1.

FX Options(I): Basics

Dr. J.D. HanKing’s College, UWO

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1.History of 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

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• A New PHLX ‘Word Currency Option’ is created at the NASDAQ.

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2. Food for Thought:

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.

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3. Characteristics of Options1) 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.

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2) Buyer versus SellerOption buyers are ‘owners’, and are said to be

“long”

Option sellers are ‘writers’, and are said to be

“short”

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3) Call versus Put• Call options :

A buyer has a right to buy at pre-set price:

<->A seller has an obligation to sell<->A seller has an obligation to sell

• Put options :

A buyer has a right to sell at the ‘strike price’:

<->A seller has an obligation to buy

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• 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.

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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.

• Land

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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)

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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 St+1.

• If X< St+1, you exercise the option contract and buy the FX at X.

• If X>St+1, you can buy the FX cheaper at the spot market than thought the option contract. You just forget about the option contract.

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* Food for Thought.If you expect the price of a certain currency to go up in the future(more

than any other people might think), what option would you buy? (circle one for the answer)

You are buying (call/put) option of that currency at the preset 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.

You will wait the spot price of the currency to rise above the pre-set price.When the spot price goes up and above the pre-set price, you will exercise

the option to (buy/sell) the currency from the option writer, and (buy/sell) the currency at the spot market. You may make profits.

If the spot price does not go up to the pre-set price, you will simply let the deal expire. All you have lost is the premium.

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There are 4 positions

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Partners\ Option Call option Put option

Long (buyer) A right to buy at X A right to sell at X

Short (seller) An obligation to sell at X

An obligation to buy at X

3. Underlying Assets

• Equities - Stock• Equity indices• Interest rates - various maturities• Foreign Exchanges=FX• Commodities

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4. Illustration

1) Symbols employed

S (or e) = price of underlying asset ( or FOREX rates)

X = Exercise price

C = Call premium

P = Put premium

T = Time until option expires

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2) Net Pay-off

= - Premium (You pay at the beginning)

+ Gross Pay-off (your profit/Loss at t+1)

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Example 1: ‘Long Call’

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Step 1. Premium paid

St+1

Premium Paid

Zero Pay-off line

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.

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St+1

Pay-off

Long Call

X

Gross Pay-off Constraint:

Call Option Pay-off =max ( 0, St+1 - X )

Step 2: Gross Pay-off: your profit/loss at t+1

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Long Call

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St+1

Note: Exercise Price is set where net value is largerthan negative of premium

Net Payoff (Payoff - Cost) : Combining the previous 2 graphs

X

Step 3: Net Pay-off

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Example 2: Short Call:

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Short Call

Example 3: Long Put

• You are buying a Put Option by paying the premium, and the option specifies X.

Step 1:

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Paying the premium by this much

Step 2: Gross Pay-off of Put Option

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XSt+1

If St+1 turns out to be lower than X, as you have a right to sell at X to the seller, you may buy at St+1 the spot market, exercise the option, and sell at X through the option contact. Your gross profit= max { 0, X-St+1}

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

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Example 4: Short Put

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X

Note that Options are symmetrical: Put Call

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Long

Short

Pay-offs of

5. Uses of Options1) Hedging: 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.

How?

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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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An Example of a 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.

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