Foreign Currency Derivatives - New York University...

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Currency DerivativesCurrency Derivatives

(or chapter 7)(or chapter 7)

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Agenda

How forex futures quoted & used for speculation?

Futures vs. forwards?

How forex options are quoted?

Speculate w/ forex options.

Distinction b/n buying & writing options?

How forex options are valued?

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Forex Futures Future delivery of standard amount of currency @ fixed time &

price. Traded @ Chicago Mercantile Exchange (CME). Specifications:

• Size –notional principal, in even multiple.• Method of stating exchange rates – “American terms” used. • Maturity date –mature on 3rd Wed/ 01, 03, 04, 06, 07, 09, 10, or 12.• Last trading day – contracts may trade through 2nd business day

prior to maturity.• Collateral & maintenance margins –purchaser/trader must deposit

initial margin or collateral.– Daily marked-to-market

• Settlement– round turn fee.

• Use of a clearing house as a counterparty

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Futures SpeculationMaturity Open High Low Settle Change High Low

Open Interest

Mar .10953 .10988 .10930 .10958 --- .11000 .09770 34,481

June .10790 .10795 .10778 .10773 --- .10800 .09730 3,405

Sept .10615 .10615 .10610 .10573 --- .10615 .09930 1,4181

Source: Wall Street Journal, February 22, 2002, p.C13

500,000 New Mexican pesos.

Short Position – believes that the value of the Peso will fall

Long Position - believes that the value of the Peso will rise

Value at maturity (Short) = - Principal (Spot – Future)

= -PS 500,000 ($0.09500/ PS - $.10958/ PS) = $7,290,

assuming spot rate of $.09500/Ps @ maturity.Value at maturity (Long) = Principal (Spot – Forward)

= PS 500,000 ($0.11000/ PS - $.10958/ PS) = $210,

assuming spot rate of $.11000/Ps @ maturity.

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Forex Futures vs. Forwards

Characteristic Foreign Currency Futures ForwardContract Size Standardized any size desiredMaturity fixed maturities any maturity up

up to a yearLocation organized exchange b/n individuals &

banks

Pricing open outcry bid/ask quotes

Margin/Collateral daily marked to market no collateral

Settlement rarely delivered, settlement contract delivered, through offsetting can offset position

Fees single commission for purchase& sell bid/ask spread

Trading hours exchange hours 24 hours

Counterparties through clearing house direct contact

Liquidity very liquid liquid, relatively large market

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Initial Margin Requirements Held as collateral by broker. Usually 2-4% of contract value. Margin amount same for short & long positions. Buyer holds a long position (seller – short). If settlement price higher than yesterday, buyer has a

positive settlement for the day. Long position now worth more. Exact opposite for seller (zero-sum game).

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Open Interest

•Open Interest refers to the number of contracts outstanding for a particular delivery month. •Initially open interest is zero. •Increases over time, until positions are liquidated. •Total open interest is the total number of outstanding positions in all the delivery months of a futures market.

•Liquidity = at least 5,000 outstanding contracts.

http://www.activetradermag.com/futuresbasics.htm

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Reversing Trades Rare in forward markets –90% of all contracts lead to

delivery. Common in futures markets – only 1% of contracts

lead to delivery!

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Forex Option Gives right but not obligation to buy/sell amount of currency

@ fixed price for given time period• Call – buyer has right to purchase• Put – buyer has right to sell• Buyer = holder & seller = writer.

Two option types• American: may exercise during life of option.• European: may not exercise until maturity.

Price elements• Strike (exercise price): exchange rate @ which foreign currency

can be purchased/ sold.• Premium, price of option• Spot rate

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Forex Options May be classified as:

• At-the-money (ATM): exercise price = spot rate.• In-the-money (ITM) options profitable, excluding

premium, if exercised immediately.• Out-of-the-money (OTM) options not profitable,

excluding premium, if exercised immediately. Markets for derivatives:

• OTC Market• Organized exchanges - Chicago Mercantile and the

Philadelphia Stock Exchange– Option Clearinghouse Corporation

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Futures Contracts vs. Options Futures Contract – you’ve agreed to

purchase/sell the contract. No backing out. Can offset/ exit by buying/selling to someone else.• Buy = long; sell = short.

Option – contract that gives you the right but not the obligation to purchase/sell something at pre-specified terms. No commitment.

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Forex Options Markets Swiss Franc options (WSJ)

Call premium: SF 62,500 x $0.0050/SF = $312.50.

Options & Underlying Strike Price Aug Sep Dec Aug Sep Dec

58.51 56 -- -- 2.76 0.04 0.22 1.1658.51 56 1/2 -- -- -- 0.06 0.30 --58.51 57 1.13 -- 1.74 0.10 0.38 1.2758.51 57 1/2 0.75 -- -- 0.17 0.55 --58.51 58 0.71 1.05 1.28 0.27 0.89 1.8158.51 58 1/2 0.50 -- -- 0.50 0.99 --58.51 59 0.30 0.66 1.21 0.90 1.36 --

Calls - Last Puts - LastEach option = 62,500 Swiss francs.

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Speculation Assume spot rate: $0.5851/SF, 6m forward: $0.5760/SF. Spot market

• $100,000. Expect six month spot SF $0.6000/SF.• Step 1: purchase SF 170,910.96 @ spot $0.5851/SF.• Step 2: sell at target spot rate of $0.60/SF.

Forward market• Step 1: Buy forward SF173,611.11 x $0.576/SF=

$100,000.• Step 2: In 6m, fulfill forward & sell proceeds in spot

market Sfr173,611.11 x $0.6000/Sfr = $104,166.67. Options market

• Long Call, Short Call, Long Put, Short Put.

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For Example… Suppose that:

• you have $10 m.• Wish to speculate on Euro• S = $ 0.885/ EUR, F30 = $ 0.900/ EUR.

– You expect S30 = $ 0.844/ EUR (EUR depreciates).– Arbitrage strategy?

– You expect S30 = $ 0.944/ EUR (EUR appreciates).– Arbitrage strategy?

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Profit & Loss Buyer of Call (Long Call)

Loss

Profit (US cents/SF)

+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5Limited loss

Unlimited profit

Break-even price

Strike price

OTM ITM

ATM

Spot price(US cents/SF)

Profit = Spot rate – (Strike price + Premium)

Profit = ? if Spot = $ 0.595/ SF.

CeT = Max[ST - E, 0]

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Profit & Loss Writer of Call (Short Call)

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5

Limited profit

Unlimited loss

Break-even price

Strike priceATM


Profit = Premium – (Spot rate - Strike price).


CeT = Max[ST - E, 0]

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Profit & Loss for Buyer of Put (Long Put)

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5Limited loss

Profit upto 58.0

Strike price

“In the money” “Out of the money”

“At the money”


Break-evenprice

Profit = Strike price – (Spot rate + Premium)


PaT=PeT=Max[E - ST, 0]

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Profit & Loss for Writer of Put (Short Put)

Loss


+ 1.00

+ 0.50

0

- 0.50

- 1.00

57.5 58.0 59.0 59.558.5

Unlimited lossup to 58.0

Limited profit

Strike price


Break-evenprice

“At the money”

Profit = Premium – (Strike price - Spot rate)


PaT=PeT=Max[E - ST, 0]

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For Example… Suppose that:

• You wish to speculate on fall of Yen vs. $.• Current S = Yen 120/ $ (or $.00833/Yen).• Maturity: 90 days.• Expected S90 = Yen 140/$ (or $.00714).• Two options available:

Call on Yen Put on Yen– Strike: Yen 125/$ Yen 125/$.

(or $.008/ Yen) (or $.008/ Yen)– Premium: $.00046 $.00003

1. What option to buy?2. Break even price on option of choice?3. If S= Yen 140/ $, what is net profit?

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Option Pricing Market value = Time value + Intrinsic Value Intrinsic Value –gain if option exercised

immediately. Will reach zero when the option is OTM. At maturity, option value = intrinsic value.

Time Value – reflects a gamble that the option might be more profitable (more in-the-money) as time passes (i.e. before time of expiry).

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1.69 1.70 1.71 1.72 1.731.681.671.660.0

1.0

2.0

3.0

4.0

5.0

Spot rate ($/£)

Option Premium(US cents/£)

6.0

1.74

4.00

Intrinsic value

3.30

5.67

1.67

Total value

Time value

-- Valuation on first day of 90-day maturity --

Strike Price of $1.70/£

Market-, Time- & Intrinsic Value

European Call on Brit Pound

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Option Volatility Standard deviation of daily % changes in underlying

exchange rate, usually stated per annum, e.g. 12.6 %.• Can obtain daily volatility

Volatility estimates:• Historic.• Forward-looking.• Implied.

%66.0105.19

%6.12365

%6.12

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Replicating Portfolio Evaluation Suppose US$-EUR rate is S0($/EUR) = $1.

S1($/ EUR) is $1.10 or $0.90. Consider call w/ K=$1/EUR (exercise price). Can replicate payoffs of call w/ levered position in EUR. Borrow PV $.90 today & buy1 EUR. Net payoff: $0.20 or $0. Portfolio value: so option value:

$1$0.90

$1.10S0($/EUR) S1($/EUR) C1($/EUR)

$0.10

$0

Debt Portfolio

-$0.90

-$0.90

$0.20

$0.00

)1(90$.1$

$i

)1(

90$.1$21

$0 i

C

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Rogue Trading: Good Fellas… Nick Leeson @ Barings.

• 1995, managed to bankrupt Barings Brothers (UK). John Rusnak @ Allied Irish Bank.

• 2002, lost $691 m on behalf of Allied Irish Bank (Baltimore office).

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Things to remember Futures terminology. Futures vs. Forwards. Speculation

• In spot & forward markets.• In option markets.

How forex options are quoted? Distinction b/n buying & writing options. How forex options are valued?

Foreign Currency Derivatives - New York University...

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