Lecture 5: Foreign Currency Options
Chapter 5: Foreign Currency Options
Overview
1.
2.
3.
4.
Definitions
Markets for Options
Speculation with Options
Option Pricing and Valuation (as time permits.)
Suggested Problems & Exercises: All
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Lecture 5: Foreign Currency Options
Definitions
An option is a contract which gives the right (but not the obligation) to buy or
sell a fixed quantity of currency at a predetermined price.
• The predetermined price is called the strike price or exercise price. (X)
• The price of the option (i.e. the cost of the contract) is called the premium.
An option that gives the holder the right to buy is called a call option.
An option that gives the holder the right to sell is called a put option.
The holder of an option is said to have a long position or be long the option.
The writer of the option is said to have a short position or be short the option.
European options may only be exercised at maturity.
American options may be exercised at any time until maturity.
• These names are archaic.
Both types are freely traded in both places, and elsewhere.
An option which would be profitable if exercised immediately is in the money.
An option which would make losses if exercised immediately is out of the money.
An option whose exercise price = the spot price is at the money.
Revision Date: October 2, 2001
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Lecture 5: Foreign Currency Options
Options (cont.)
Example
You’ve bought a call option for 100,000 DEM with an exercise price of 0.50
USD/DEM and a maturity date of June 30th. The seller of the option (your
counterparty) is the Royal Bank of Canada.
You are long the call; RBC is short the call.
• You get to choose whether to exercise the option, therefore you are long.
• RBC has a obligation to honour your choice, therefore they are short.
For simplicity, suppose it’s a european option.
If the spot rate on June 30th is 0.55 USD/DEM, we’ll exercise the option.
• It lets us buy DEM for 0.50 each instead of 0.55
so we save 0.05 x 100,000 = $5,000.
If the spot rate on June 30th is 0.48 USD/DEM, we’ll just let the option expire.
• If we want to buy DEM, it’s cheaper to use the spot rate than to exercise the
option.
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
FX Derivatives in OTC Markets
Definition: OTC (Over-the-counter) markets are ones where financial
intermediates (mostly large banks) offer various foreign exchange products
tailored to their customer’s needs.
Definition: FX Derivatives include fx forwards, fx swaps and fx options.
As a client, you can get contracts for pretty much any currency, maturity date,
amount (and strike price for options.) However,
• maturities over one year are less common.
• amounts are typically for between 1M and 10M USD.
• big currencies most popular (e.g. USD vs EUR, GBP, CHF, JPY, CAD)
• at or near-the money options are most popular.
• bid-ask spreads may be much wider for uncommon stuff.
OTC option contracts usually stipulate that the bank is prepared to repurchase
the option at their posted prices. This usually doesn’t apply to swaps and
forwards; once you buy them, you’re typically stuck with them until they expire.
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Lecture 5: Foreign Currency Options
FX Derivatives in OTC Markets (cont.)
We can add another ~100 Billion USD if we include OTC FX derivatives
That’s the value of OTC trading volume in currency options and swaps.
• That compares to a global total OTC trading volume in all derivatives of $362
• The difference is interest rate derivatives (FRAs, swaps, options, etc.)
The FX derivatives market is a small fraction of the total FX market,
but it is growing faster.
Grew at an annual rate of 29% from 1995 to 1998! (More than doubled.)
• All OTC derivatives grew at an annual rate of 23% over that period.
Of all the OTC market derivative activity in 1998
• 36% was in the U.K.
• 19% was in the U.S.
• 10% was in France
• 9% was in Japan
• 7% was in Germany.
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Exchange-Traded FX Derivatives
The alternative to the OTC market is the exchange-traded contract.
These contracts are traded on an organized exchange with a specific location.
• Applies to both futures contracts (just like forwards) and options.
• see www exercise #2 at end of chapter.
OTC trading is mostly between banks and MNEs covering fx risk.
Exchange trading is mostly investors/speculators and banks.
• Individuals drawn to exchanges by accessability.
• Banks use exchanges to balance their risk after dealing with clients.
The Philadelphia Exchange was on of the pioneers in fx option trading.
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Options on the PHLX
Currenciesa
Contract amounts
USD / AUD
50,000
AUD
USD / GBP
31,250
GBP
USD / CAD
50,000
CAD
USD / DEM
62,500
DEM
USD / ECU
62,500
ECU
USD / FRF
250,000
FRF
USD / JPY
6,250,000
JPY
USD / CHF
62,500
CHF
DEM / JPY
62,500
DEM
GBP / DEM
31,250
GBP
a. As of Jan. 1999
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Lecture 5: Foreign Currency Options
Options on the PHLX (cont.)
Type: The default is European options. American options are also available for
all but the longest terms.
Maturity: PHLX trades options contracts for each of the next three months,
March, June, September, December, the following June and the following
December.
• e.g. In Jan. 1999, they’re trading option contracts which expire in Feb., Mar.,
Apr., Jun., Sep. and Dec. 1999, Jun. 2000 and Dec. 2000.
Two maturity dates per month.
• mid-month options are settled on the third Wednesday of the month and stop
trading the Friday before.
• month-end options stop trading on the last Friday of the month and settle on
the following Wednesday.
Strike Prices: Strike prices are set (in intervals of, say $0.005 USD) around the
current spot rate. The longer the maturity, the wider the range of strike prices.
• When spot rates move, new contracts may be added and commence trading.
Revision Date: October 2, 2001
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Lecture 5: Foreign Currency Options
Default Risk and Organization
Default Risk: The risk that your counterparty will not fulfil the terms of your
contract. (Also known as counterparty risk.)
• They refuse to sell (buy) the amount specified at the time and price specified.
• A contract with a large default risk is a (near-) worthless contract.
OTC markets guard against default risk using size and reputation.
• You buy contracts from long-established, big international banks.
In OTC markets, contracts are illiquid because people care about the quality of
their counterparties.
• You cannot freely sell your outstanding contracts to just anyone, since your
counterparty would rightfully be concerned if that new person were likely to
default.
• Everyone gets to determine which counterparties they will accept
(just like in the interbank FX market.)
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Lecture 5: Foreign Currency Options
Liquidity and Standardization
Exchange Markets solve the problem of contract liquidity
Exchanges make it easy to buy and sell positions freely and rapidly at low
transaction costs (typically lower than in OTC markets.) Two features are key.
Standardization: Contracts are standardized in terms of currency, maturity
dates, amounts (and strike prices in the case of options.)
Exchanges also insure against default risk.
• All contracts traded on a given exchange are contracts with the same
counterparty; the exchange’s clearing house.
• Therefore, even if individual participants go broke, your contract is not
affected unless the clearing house goes broke.
How do you protect the clearing house from going broke?
If people with money-losing contracts tend to go broke, the clearing house will
tend to have to pay more than it receives.
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Lecture 5: Foreign Currency Options
Margin deposits
In order to obtain futures or options contracts, you must make a deposit
(i.e. post a performance bond) with the clearing house.
If you fail to meet your financial obligations, you lose this “margin” deposit.
• This gives you a financial incentive to honour your commitments.
Marking to Market: Every night, after trading ceases for the day, the exchange
adjusts the balance of your margin deposit.
• falls in the market value of your contracts are subtracted from the deposit.
• rises in the market value of your contracts are added to the deposit.
Margin calls: When the balance of your deposit reaches a minimum threshold
(the “maintenance level”), you are required to add more money in order to raise
the balance back to the initial level. (a “margin call.”)
• If you don’t, all your positions are liquidated and your account is settled.
Under this system, the most the exchange stands to lose from defaults are a
single’s day’s losses, less the amount of the maintenance margin.
Revision Date: October 2, 2001
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École des Hautes Études Commerciales, Montréal
Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Margins on Futures and on Options
Margins work differently on futures and option contracts.
For futures contracts, you always have to maintain a margin.
• Margin usually maintained in USD.
For long option positions, you don’t have to maintain a margin.
• You pay the premium up front.
• Thereafter, you have no further potential losses, so the clearing house doesn’t
have to worry about you defaulting on your obligations.
For short option positions, you have to maintain a margin.
• You receive the premium up front.
• Thereafter you have nothing but potential losses, so the clearing house
worries a lot about margin requirements.
Major changes in market volatility will often change margin requirements.
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
FX Option Prices and Quotes
See Exhibit 5.1
Note direct quotes! This is standard with options.
Column 1: The price of the underlying asset -- spot USD/CHF.
Column 2: Strike Price -- option allows you to buy 1 CHF for $0.5850 USD.
Column 3: Premium -- price paid per CHF for the option.
• Standard CHF option is 62,500 CHF so cost of 1 contract
= 62,500 CHF x $0.0050 USD/CHF = $312.50
• missing values indicate those options did not trade that day.
Think: Why does the value of calls fall as we move down the table, but those of
puts rises?
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Speculating with Options
Holders of options face limited loss but unlimited gains (just like stocks.)
Writers of options face limited gains but unlimited losses (just like insurance.)
Exhibit 5.2 considers the call option from Exhibit 5.1
• strike price is $0.585 USD/CHF
• option premium is $0.005 USD/CHF
• will be exercised at maturity if spot rate > $0.585, not if < $0.585
Breakeven is $0.59 USD/CHF
• S > $0.59 means Willem Koopmans makes money.
• S < $0.59 means Willem Koopmans’ banker makes money.
Exhibit 5.3 considers the put option from Exhibit 5.1
Breakeven price is now $0.58 USD/CHF.
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Option Valuation
Option Premium = Intrinsic Value + Temporal Value (or Time Value)
Intrinsic Value: Amount earned by exercising the option at current spot rate.
• This is Max(0,S-X) for a call, Max(0,X-S) for a put.
• Doesn’t necessarily mean you are able to exercise it right away.
Temporal Value: Option premium - Instrinsic Value
• reflects the chances of being deeper in the money when exercised.
See Exhibit 5.4
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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Lecture 5: Foreign Currency Options
Sensitivity of Option Prices
Summarized in Exhibit 5.11
Delta: Sensitivity of option value to spot rate.
• Always between 0 and 1.
• Closer to 0 for deep out-of-the-money, closer to 1 for deep in-the-money.
Theta: Sensitivity to time-to-maturity.
Lambda: Sensitivity to volatility.
Comparing Exhibits 5.6 and 5.7, we see that these two have similar effects.
• What matters is total uncertainty over the remaining life of the option.
• This is jointly determined by volatility & remaining duration.
Strike Price: The deeper in-the-money, the higher the value.
• no greek name
You may skip the other factors (rho, phi, and forward rates.)
Revision Date: October 2, 2001
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Copyright 2001 by Simon van Norden
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