Multinational Business Finance

Foreign Currency DerivativesFutures and Forwards, and options

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Adapted from ESM bookYinghong.chen@liu.se

Foreign exchange derivatives

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“Well, it helps to look at derivatives like atoms. Split them one way and you have heat and energy - useful stuff. Split them another way and you have a bomb. You have to understand the subtleties.”

Kate JenningsMoral Hazard, 2002, p. 8

Introduction to Forward Contracts

• Both futures and forwards specify a trade between two counter-parties:– The seller (or the short) makes a commitment to deliver

an asset, at a specified forward price.– the buyer (or the long) makes a commitment to take

delivery of an asset, at a specified forward price.– At delivery, cash is exchanged for the asset.

©David Dubofsky and 4-4 Thomas W. Miller, Jr.

Futures and Forwards: A Comparison

Default Risk: Borne by Clearinghouse Borne by Counter-Parties

What to Trade: Standardized NegotiableThe Forward/Futures Agreed on at Time Agreed on at Time

Price of Trade Then, of Trade. Payment atMarked-to-Market Contract Termination

Where to Trade: Standardized NegotiableWhen to Trade: Standardized NegotiableLiquidity Risk: Clearinghouse Makes it Cannot Exit as Easily:

Easy to Exit Commitment Must Make an EntireNew Contract

How Much to Trade: Standardized Negotiable

What Type to Trade: Standardized Negotiable

Margin Required Collateral is negotiable

Typical Holding Pd. Offset prior to delivery Delivery takes place

Futures Forwards

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Futures Contract - Example

Specification of the Australian Dollar futures contract (International Money Market at CME)

Size AUD 100,000Quotation USD / AUDDelivery Month March, June, September,

December Min. Price Move $0.0001 ($10.00)Settlement Date Third Wednesday of delivery

monthStop of Trading Two business days prior to

settlement date

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Futures - The Clearing House

When A “sells” a futures contract to B, the Clearing House takes over and the result is: A sells to the Clearing House Clearing House sells to B

The Clearing House keeps track of all transactions that take place and calculates the “net position” of all members.

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Futures - Marking to Market

Futures contracts are “marked to market” daily. Generates cash flows to (or from) holders of foreign

currency futures from (or to) the clearing house. Mechanics:

Buy a futures contract this morning at the price of f0,T

At the end of the day, the new price is f1,T The change in your futures account will be:

[f1,T - f0,T] x Contract Face Value = Cash Flow

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Purpose of Marking to Market

Daily marking to market means that profits and losses are realized as they occur. Therefore, it minimizes the risk of default.

By defaulting, the investor merely avoids the latest marking to market outflow. All previous losses have already been settled in cash.

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Marking to Market – Example

Trader buys 1 AUD contract on 1 Feb for USD0.5000/AUD

USD value = 100,000 x 0.5000 = USD 50,000.

Date Settlement Value of Contract Margin A/c________________________________________________________________________________

1 Feb 0.4980 49,800 - 200 2 Feb 0.4990 49,900 + 100 3 Feb 0.5020 50,200 + 300 4 Feb 0.5010 50,100 - 100

Forward Contracts:Payoff Profiles

profit profit

S(T) S(T)

The long side gains if the spot price atdelivery, S(T), exceeds the originalforward price, F(0,T).

The short side gains if the price atdelivery, S(T), is below the original forward price, F(0,T).

Long forwardShort forward

F(0,T) F(0,T)

Profits for Forward Contracts• If S(T) > F(0,T), the long side gains by S(T) - F(0,T) per unit, and the short side

loses this amount.

• If S(T) < F(0,T), the short side profits by F(0,T) - S(T) per unit, and the long loses this amount.

• Example: You sell ¥20 million forward at a forward price of $0.0090/ ¥. At expiration, the spot price is $0.0083/ ¥.

– Did you profit or did you lose? – How much?

Default Risk for Forwards, I.• If the forward price is “fair” at initiation:

– The contract is valueless.– There is no immediate default risk.

• As time goes by, the forward price (for delivery on the same date as the original contract subsequently) can change:– Existing forward contracts acquire value: They become an asset for

one party and a liability for the other.– Default risk appears. – (Q: Which party faces default risk?)

Default Risk for Forwards (cont.)

• At any time, only one counter-party has the incentive to default.

• It is the counter-party for whom the forward contract has become a liability.

• The amount exposed to default risk at time t is: PV{ F(0,T) - F(t,T) }, 0 < t < T

Recall from Corporate finance the present value of a future outlay = Discounted cash flow to the present time.

Example: Default Risk for Forwards

On April 4th, you buy 100,000 bbl of oil forward at a forward price of $27/bbl. The delivery date is July 4th. On May 4th, the forward price for delivery on July 4th is $23/bbl.

– Who has the incentive to default?

– If the interest rate on May 4th for 2-month debt instruments is 5%, what is the dollar amount exposed to default risk?

The expected loss amount is the loss that might materialize at the expiration day, 2 month from now, if the spot price stays at 24$, the total expected loss is 3$*100,000=300,000 $ discounted at 5% “2 month yield) =1/(1+0.05)*300,000=5714.286$. The dollar amount that is exposed to default risk is 5714.286$.

Forward Rate Agreements (FRAs)

• A FRA is a forward contract on an interest rate (not on a bond, or a loan).

• The buyer of a FRA profits from an increase in interest rates. The seller of a FRA profits from a decline in rates.

• The buyer effectively has agreed to borrow an amount of money in the future at the stated forward (contract) rate. The seller has effectively locked in a lending rate.

• FRA’s are cash settled.

Forward Rate Agreements (FRAs)

• Only the difference in interest rates is paid. The principal is not exchanged.

• FRAs are cash settled.

0 t1 t2

Loan periodorigination date

settlement date, or delivery date

end of forward period

Forward Rate Agreements (FRAs)

• If the spot rate at delivery (“settlement rate”, r(t1,t2)) exceeds the forward rate agreed to in the FRA (“contract rate” = fr(0,t1,t2), the FRA buyer profits.

• The amount paid (at time t1) is the present value of the difference between the settlement rate and the contract rate times the notional principal times the fraction of the year of the forward period.

• A FRA’s value is initially zero, when the contract rate is the theoretical forward rate. Subsequently, forward rates will change, so the FRA will have positive value for one party (and equally negative value for the other).

Part II Foreign Currency Derivatives

These instruments can be used for two very distinct management objectives: Speculation – use of derivative instruments to take a position in the

expectation of a profit Hedging – use of derivative instruments to reduce the risks associated

with the everyday management of corporate cash flow

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Foreign Currency Derivatives• Derivatives are used by firms to achieve one of more

of the following individual benefits:– Permit firms to achieve payoffs that they would not be

able to achieve without derivatives, or could achieve only at greater cost

– Hedge risks that otherwise would not be possible to hedge– Make underlying markets more efficient (price discovery)– Reduce volatility of stock returns (by writing call options on

stocks you own)– Minimize earnings volatility (hedging against currency risk)– Reduce tax liabilities (if capital gains tax is lower)– Motivate management (agency theory effect)

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Foreign Currency Futures• A foreign currency futures contract is an alternative

to a forward contract that calls for future delivery of a standard amount of foreign exchange at a fixed time, place and price.

• It is similar to futures contracts that exist for commodities such as cattle, lumber, interest-bearing deposits, gold, etc.

• In the US, the most important market for foreign currency futures is the International Monetary Market (IMM), a division of the Chicago Mercantile Exchange (CME).

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Foreign Currency Futures• Major features that are standardized are:

1. Contract size2. Method of stating exchange rates3. Maturity date4. Last trading day5. Collateral and maintenance margins6. Settlement7. Commissions8. Use of a clearinghouse as a counterparty

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Foreign Currency Futures• Foreign currency futures contracts differ from forward contracts in a

number of important ways:– Futures are standardized in terms of size while forwards can be

customized– Futures have fixed maturities while forwards can have any maturity

(both typically have maturities of one year or less)– Trading on futures occurs on organized exchanges while forwards are

traded between individuals and banks– Futures have an initial margin that is market to market on a daily basis

while only a bank relationship is needed for a forward– Futures are rarely delivered upon (settled) while forwards are

normally delivered upon (settled)

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Foreign Currency OptionsA foreign currency option is a contract giving the

option purchaser (the buyer) the right, but not the obligation, to buy or sell a given amount of foreign exchange at a fixed price per unit for a specified time period (until the maturity date).

There are two basic types of options, puts and calls. A call is an option to buy foreign currency A put is an option to sell foreign currency

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Foreign Currency Options• The buyer of an option is termed the holder.• the one who writes the option is referred to as the writer or

grantor.• Every option has three different price elements:

– The exercise or strike price – the exchange rate at which the foreign currency can be purchased (call) or sold (put)

– The premium – the price, or value of the option itself– The underlying spot exchange rate in the market

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Foreign Currency Options

• An American option gives the buyer the right to exercise the option at any time between the date of writing and the expiration date.

• A European option can be exercised only on its expiration date, not before. (you can always sell the option at a higher price at the market because of the time value)

• The premium, or option price, is the cost of the option.

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Foreign Currency Options

• An option whose exercise price is the same as the spot price of the underlying currency is said to be at-the-money (ATM).

• An option the would be profitable, excluding the cost of the premium, if exercised immediately is said to be in-the-money (ITM).

• An option that would not be profitable, excluding the cost of the premium, if exercised immediately is referred to as out-of-the money (OTM)

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Call Put

Intrinsic value max(ST - X, 0) max(X - ST, 0)

in the money ST – X > 0 X – ST > 0

at the money ST – X = 0 X – ST = 0

out of the money ST – X < 0 X – ST < 0

Time Value CT – Int. value PT – Int. value

Option Pricing & Valuation

An example: buy a call on Swiss Franc

Buyer of a call:– Assume purchase of August call option on Swiss francs

with strike price of 58½ ($0.5850/SF), and a premium of $0.005/SF

What happens at the expiration day?

Note, the strike price is important, it is the price you choose to buy the asset if exercised. Your profit is Spot rate in the market-strike price at the expiration day.

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Exhibit 8.4 Buying a Call Option on Swiss Francs

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Exhibit 8.5 Writing a Call Option on Swiss Francs

Foreign Currency Speculation• Speculation is an attempt to profit by trading on expectations

about prices in the future.• Speculators can attempt to profit in the:

– Spot market – when the speculator believes the foreign currency will appreciate in value

– Forward market – when the speculator believes the spot price at some future date will differ from today’s forward price for the same date

– Options markets – volatile market, buy or sale of put and/or call

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Option Market Speculation• Writer of a call:

– The maximum profit that the writer of the call option can make is limited to the premium

– If the writer wrote the option naked, that is without owning the currency, the writer would have to buy the currency at the spot at the expiration day and take the loss to deliver at the strike price

– The amount of such a loss is unlimited and increases as the underlying currency rises

– Even if the writer already owns the currency, the writer will experience an opportunity loss

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Option Market Speculation• Buyer of a Put:

– The basic terms of this example are similar to those just illustrated with the call

– The buyer of a put option, however, wants to be able to sell the underlying currency at the exercise price $0.585/SF when the market price of that currency drops

– If the spot price drops to $0.575/SF, the buyer of the put will deliver Swiss francs to the writer and receive $0.585/SF

– At any exchange rate above the strike price of 58.5, the buyer of the put would not exercise the option, and would lose only the $0.005/SF premium

– The buyer of a put (like the buyer of the call) can never lose more than the premium paid up front

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Exhibit 8.6 Buying a Put Option on Swiss Francs

Option Market Speculation

• Seller (writer) of a put:– In this case, if the spot price of francs drops below 58.5

cents per Swiss franc, the option will be exercised– Below a price of 58.0 cents per Swiss franc, the writer

will lose more than the premium received from writing the option (falling below break-even)

– If the spot price is above $0.585/SF, the option will not be exercised and the option writer will pocket the entire premium

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Exhibit 8.7 Selling a Put Option on Swiss Francs

Option Pricing and ValuationThe pricing of any currency option combines six

elements: Present spot rate Time to maturity Forward rate for matching maturity US dollar interest rate Foreign currency interest rate Volatility (standard deviation of daily spot price

movements)

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Option Pricing and Valuation• The total value (premium) of an option is equal to the

intrinsic value plus time value.• Intrinsic value is the financial gain if the option is exercised

immediately.– For a call option, intrinsic value is zero when the strike

price is above the spot price– When the spot price rises above the strike price, the

intrinsic value become positive On the date of maturity, an option will have a value equal to its intrinsic value (zero time remaining means zero time value)

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Currency Option Pricing Sensitivity

• The time value of an option exists because the price of the underlying currency, the spot rate, can potentially move into the money between the present time and the option’s expiration date.

• If currency options are to be used effectively, either for the purposes of speculation or risk management, the individual trader needs to know how option values – premiums – react to their various components.

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Currency Option Pricing Sensitivity• Forward rate sensitivity:

– Standard foreign currency options are priced around the forward rate because the current spot rate and both the domestic and foreign interest rates are included in the option premium calculation

– The option-pricing formula calculates a subjective probability distribution centered on the forward rate

– This approach does not mean that the market expects the forward rate to be equal to the future spot rate, it is simply a result of the arbitrage-pricing structure of options

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Currency Option Pricing Sensitivity

• Spot rate sensitivity (delta):– The sensitivity of the option premium to a small

change in the spot exchange rate is called the delta

delta =

– The higher the delta, the greater the probability of the option expiring in-the-money

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Δ spot rateΔ premium

Currency Option Pricing Sensitivity

• Time to maturity – value and deterioration (theta):– Option values increase with the length of time to

maturitytheta =

– A trader will normally find longer-maturity option better values, giving the trader the ability to alter an option position without suffering significant time value deterioration

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Δ timeΔ premium

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Option Pricing & Valuation

Exhibit 8.11 Theta: Option Premium Time Value Deterioration

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Currency Option Pricing Sensitivity

• Sensitivity to volatility (lambda):– Option volatility is defined as the standard deviation of daily

percentage changes in the underlying exchange rate– Volatility is important to option value because of an exchange rate’s

perceived likelihood to move either into or out of the range in which the option will be exercised

lambda =

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Δ volatilityΔ premium

Currency Option Pricing Sensitivity• Volatility is viewed in three ways:

• Historic • Forward-looking• Implied

• Because volatilities are the only judgmental component that the option writer contributes, they play a critical role in the pricing of options.

• All currency pairs have historical series that contribute to the formation of the expectations of option writers.

• In the end, the truly talented option writers are those with the intuition and insight to price the future effectively.

• Traders who believe that volatilities will fall significantly in the near-term will sell (write) options now, hoping to buy them back for a profit immediately volatilities fall, when the option premiums falls.

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Currency Option Pricing Sensitivity• Sensitivity to changing interest rate differentials (rho and phi):

– Currency option prices and values are focused on the forward rate– The forward rate is in turn based on the theory of Interest Rate Parity– Interest rate changes in either currency will alter the forward rate, which

in turn will alter the option’s premium or value• A trader who is purchasing a call option on foreign currency should do so

before the domestic interest rate rises. This timing will allow the trader to purchase the option before its price increases.

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Currency Option Pricing Sensitivity• The expected change in the option premium from a small

change in the domestic interest rate (home currency) is the term rho.

rho =

• The expected change in the option premium from a small change in the foreign interest rate (foreign currency) is termed phi.

phi =

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Δ US $ interest rateΔ premium

Δ foreign interest rateΔ premium

Exhibit 8.13 Interest Differentials and Call Option Premiums

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Currency Option Pricing Sensitivity

• The sixth and final element that is important to option valuation is the selection of the actual strike price.

• A firm must make a choice as per the strike price it wishes to use in constructing an option (OTC market).

• Consideration must be given to the tradeoff between strike prices and premiums. See next slide.

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Exhibit 8.14 Option Premiums for Alternative Strike Rates

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Exhibit 8.15 Summary of Option Premium Components

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Mini-Case Questions: Warren Buffett’s Love-Hate Relationship with Derivatives

• In his 2002 letter to shareholders, what does Warren Buffett seem to fear most about financial derivatives?

• In his 2007 letter to shareholders, what does Warren Buffett admit that he and Charlie had done?

• Do you think there is an underlying consistency in his viewpoint on the proper use of derivatives?

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Exhibit 8.1 Mexican Peso Futures, US$/Peso (CME)

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Exhibit 8.2 Currency Futures and Forwards Compared

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Exhibit 8.3 Swiss Franc Option Quotations (U.S. cents/SF)

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Exhibit 8.8 Analysis of Call

Option on British Pounds with a Strike Price =

$1.70/£

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Exhibit 8.9 The Intrinsic, Time, and Total Value Components of the 90-Day Call Option on British Pounds at Varying Spot Exchange

Rates

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Exhibit 8.10 Decomposing Call Option Premiums: Intrinsic Value and Time Value

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Exhibit 8.12 Foreign Exchange Implied Volatility for Foreign Currency Options, January 30, 2008