1. Options
Unlike futures and forwards, options give the holder the right, but not the obligation, to either
buy or sell the underlying commodity at a fixed price called the exercise or strike price.
American style options may be exercised at any time up to contract expiration. European
options can only be exercised at maturity. Some options on the S&P500 and some currency
options are European style. Note that the style has nothing to do with trading location. A buyer
may prefer European style options because they are typically cheaper than American options.
a. Call options
A call option provides the right to buy the underlying commodity. The call buyer must pay the
option premium (C) to the call writer. The option buyer may exercise the option and purchase
the underlying spot commodity by paying the exercise or strike price (X). The option has
intrinsic value if the underlying spot price (S) is greater than X. In this case the option is said to
be ‘in the money.’ If at expiration S > X, the option will be exercised, if not the option expires
worthless. In either case, the initial call price C is a sunk cost.
Call options will not normally be exercised prior to maturity unless the underlying commodity
pays a large enough cash flow prior to maturity, even if they are in the money. This is so because
the option is worth more “alive” (unexercised) than “dead” (exercised); the option has both time
value and intrinsic value. The time value is forfeited if the option is exercised. An option holder
wishing to terminate their option position could simply sell the option instead of exercising it.
Mathematically, this is equivalent to stating that C > Max (0, S-X) for a call prior to maturity.
Purchasing a call option is a bullish strategy that makes money if the underlying commodity
price rises. Writing a call is a neutral or bearish strategy. Buying a call is a limited loss strategy
with a potentially unlimited gain, writing a call is the opposite.
Teaching Tip: Options are wasting assets, their time value erodes as expiration approaches.
Option prices are also directly related to the level of underlying spot price volatility. Thus,
buying an option is a bet that either a) the spot price will increase enough to offset the loss in
time value and/or b) the spot price volatility will increase enough to offset the loss in time value.
Teaching Tip: Comparing a call option with a spot position.
Suppose an at the money American style Swiss franc (Sfr or CHX on quote sheets) call option
has the following terms:
Exercise price 1Sfr = $0.655 Option Premium = 2¢/Sfr
Contract size = 62,500 Sfr Expiration = 90 days
This option gives the buyer the right to purchase 62,500 Sfr at any time within the next 90
days at an exercise (or strike) price of 62,500 Sfr $0.655/Sfr = $40,937.50.
The price the option buyer must pay to obtain this right (the premium) is 62,500 Sfr
$.02/Sfr = $1,250. Assuming the buyer holds the option to just before expiration for
simplicity, the investor’s profit diagram is:
Profit
Spot
ST
$0.655
This option position does not appear very risky due to the limited loss feature of the option, but it
is actually riskier than a spot position. Why?
• To compare to the option to a spot position you would have to consider an equivalent dollar
amount invested ($40,937.50) or buying 32.75 option contracts ($40,937.50/$1,250). In the
option position, you have only a few months for the currency to move or you stand to lose
100% of $40,937.50.
Teaching Tip: An investor can purchase at the money, in the money, or out of the money calls.
In the money calls will have a larger potential dollar loss but a lower breakeven than out of the
money calls. Out of the money calls are more likely to result in a loss, but may yield high
percentage rates of return if the commodity price increases significantly.
Teaching Tip: To go from a long call to a written call position simply flip the call graph vertically
upside down. The maximum loss will become the maximum gain and the positive slope line will
have a negative slope. To go from a call position to a put position with equivalent terms, flip the
graph horizontally.
Teaching Tip: A majority of options expire worthless and many institutions write calls to
generate additional income to improve their current period rate of return.
b. Put options
A put option provides the right to sell the underlying commodity. The put buyer must pay the
option premium (P) to the put writer. The option buyer may exercise the option and sell the
underlying spot commodity by delivering the commodity in exchange for the exercise or strike
price (X). The option has intrinsic value if the underlying spot price (S) is less than X. If at
expiration S < X the option will be exercised, if not the option expires worthless. In either case
the initial put price P is a sunk cost.
Similar to calls, put options will not normally be exercised prior to maturity unless the option is
deep in the money.
-$1,250 $0.675
Purchasing a put option is a bearish strategy that makes money if the underlying commodity
price falls. Writing a put is a neutral or bullish strategy. Buying a put is a limited loss strategy
with a potentially large gain, writing a put is the opposite.
Long Put
Profit
Teaching Tip: The profit diagram of any option position (or any option hedge) can be found from
a profit table as below, where 0 = time of put purchase, T = contract expiration. The breakeven is
found by setting the profit to zero and solving for ST. These tables and the associated graphs are
excellent teaching tools.
1.1 BUYING A PUT
1.1.1 Profit Table ST < E ST > E
-P0-P0-P0
+PTE- ST0
= Profit E – ST – P0-P0
Breakeven ST = E – P0
If ST does not appear in the profit equation, the profit graph is a straight line, whereas if ST is
present the sign on ST indicates the slope (positive or negative) of the line.
Writing a put
Profit
St
X
1.2 WRITING A PUT
1.2.1 Profit Table ST < E ST > E
+P0+P0+P0
-PT-(E- ST) 0
= Profit ST – E + P0+P0
Breakeven ST = E – P0
c. Option Values
The intrinsic value of a call option is the maximum of zero or S-X.
The intrinsic value of a put option is the maximum of zero or X-S.
An option also has time value because the option’s returns are asymmetric. An out of the money
option that has not yet expired may yet wind up in the money, an in the money option may wind
up further in the money. If not, the option is simply not used. As a result, normally an option is
worth more than its intrinsic value. The option’s time value is calculated as the option premium
minus the intrinsic value.
Teaching Tip: The time value is representative of the right to purchase the security or not,
depending upon whether it is profitable to do so. It literally represents the probability that the
commodity price will increase and move the option further in the money. Time value is greatest
for an at the money option. For deep out of the money options, the time to expiration provides
little likelihood that an option will be exercised; for deep in the money options, the ability to not
exercise the option has little value.
Other variables include:
: The greater the standard deviation of the value of the underlying security the greater
the option’s value. This is because the option is a right that can be used if profitable and
not used if it is not desirable.
St
X
Risk free rate (Rf): The greater the risk free rate the higher (lower) the value of a call
(put) option, ceteris paribus. This is because buying a call is an alternative to buying
stock on margin. The cost of buying stock on margin is increased by higher interest rates,
making the call alternative more valuable. Buying a put is an alternative to shorting the
underlying stock and investing the proceeds at Rf. With a higher Rf the put alternative is
relatively less valuable.
Time to expiration: Generally, the longer the time period until expiration the greater the
option’s value.
d. Option Markets
The average number of exchange trade option contracts outstanding was about $32 trillion in
2010. The value of options contracts traded worldwide in 2013 was over $9.4 trillion according
to the FIA Annual Volume Survey. From modest beginnings in 1973 with the Chicago Board
Options Exchange (CBOE), the world’s first market dedicated to options, option trading has
grown worldwide. In the U.S. options are traded similarly to futures in trading pits at open
outcry auctions. In 2000, the CBOE introduced hand held computers that greatly accelerated
order execution.
Options on individual common stocks and stock indexes are popular today for both hedgers
and speculators. Hedgers may use long put options or written call options on individual
stocks or indexes to hedge a long stock position. Stock index options are cash settled and the
major S&P500 contract is a European option. Index options allow the investor to hedge
systematic risk and partial hedges can be used to adjust a portfolio’s beta up or down.
Listed stock option contracts are for 100 shares. An AMR options quotes can be used to
illustrate:
Example January AMR options quote:
AMR Underlying stock price $8.79
Expiratio
n
Call Put
STRIK
E
LAS
T
VOLUM
E
OPEN
INTERES
T
LAS
T
VOLUM
E
OPEN
INTERES
T
May 6.00 3.30 12 578 0.45 20 4175
Jan 7.50 1.30 60 17062 0.15 138 58909
The May call is in the money and the call premium is $3.30 * 100 = $330. The intrinsic value of
the call (S-X) is ($8.79 – $6.00) * 100 = $279. The time value of the call is $330 – $279 = $51.
An investor would not exercise this call because that would be throwing away the $51 time
value. The May put is out of the money and the put’s intrinsic value (X-S) is 0. Note that the put
still has time value however equal to $0.45 * 100 = $45. Notice that the closer to the money
option has much higher open interest.
Options exist on futures contracts as well. The buyer of a call (put) option on a futures
contract has the right, but not the obligation, to purchase (sell) a futures contract at the
exercise price. Options on futures are popular because it is often cheaper to deliver the
futures contract rather than the underlying commodity. The futures contract is typically more
liquid than the underlying spot and more information about supply and demand for futures
may be available than can be easily found for the underlying commodity or security.
The Philadelphia Options Exchange offers several popular currency options contracts.
Options are available for the euro, British pound, Japanese yen, Australian dollar, Canadian
dollar and the Swiss franc.
Options may be used to limit default risk as well. Credit spread options and digital default
options are two examples:
Credit spread call options may be used to provide a payoff in the event of a loan default.
A credit spread call option pays the holder if the default risk premium or yield spread on
a specified benchmark bond of the borrower increases above some exercise spread.
A digital default option pays a stated amount, usually the par on the loan or bond in the event of
a default on the underlying credit.
2. Regulation of Futures and Options Markets
The Commodity Futures Trade Commission (CFTC) is the main regulator of futures
contracts and options on futures contracts. The CFTC seeks to eliminate trading abuses and
prevent market manipulation.
The Securities Exchange Commission (SEC) regulates options on stocks and stock indexes.
The bank regulators have guidelines for institutions to follow. A bank must have internal
hedging guidelines and policies. The bank must have derivatives trading limits and must
disclose large positions that could materially affect the bank. Regulators can mandate a bank
hold more capital to offset risk from derivatives positions. The financial crisis revealed that
regulators had not required sufficient capital to back banks’ off balance sheet derivative
activities.
Until the Dodd-Frank Act neither the SEC nor the CFTC directly regulated OTC derivatives.
Under the new law OTC derivatives may be required to be traded on an exchange and as
such would come under the purview of the SEC and CFTC. Moreover bank regulators will
presumably more tightly regulate bank usage of derivatives.
3. Swaps
A swap is an agreement whereby two parties agree to pay each other specified cash flows for a
set period of time. They are custom designed contracts primarily used to hedge currency and/or
interest rate risk. Interest rate swaps, currency swaps, credit risk swaps, commodity swaps and
equity swaps comprise the major types.
a. Interest Rate Swaps
According to the Bank of International Settlements, as of June 2013 the notional principal of
interest rate swap contracts outstanding was $425.6 trillion. Interest rate swaps are by far the
largest single component of the OTC derivatives market. The euro is the largest component of
single currency interest rate swaps at $168.7 trillion followed by the U.S. dollar at $120.3
trillion. Note that the notional principal amounts overstate the significance of the interest rate
swap market since these amounts are NOT swapped. The market value of the interest rate swap
market is a better measure of the true size and the market value was $13.7 trillion.
In a plain vanilla interest rate swap one party agrees to pay a fixed interest rate on a given
notional principal to the counterparty, and the counterparty agrees to pay a variable rate of
interest on the same notional principal. Swap maturities range from a few months to many years.
The party making a fixed interest payment may be called the swap buyer, whereas the party
making a variable payment may be called the swap seller. Principal is not normally exchanged;
hence the term notional principal designates only the amount used to calculate the dollars of
interest paid. Only net payments are actually transferred.
An institution that has too many rate sensitive liabilities relative to its holdings of rate sensitive
assets is at risk from an interest rate increase (the typical position of a mortgage lender that is
funding the mortgages with deposits). This FI may seek a swap where the FI agrees to pay a
fixed rate of interest in exchange for receiving a variable rate of interest. See the swap diagram
below. If their own liability costs rise with rising interest rates, the swap payments received will
also rise but their swap outflows are fixed. Thus, profitability is protected from an interest rate
change. Large money center banks are often willing to serve as a counterparty to a bank or thrift
in need of a swap. The intermediary banks may also act as brokers by finding a suitable
counterparty.
The term RSA is equal to rate sensitive assets, RSL is equal to rate sensitive liabilities, FRA and
FRL are fixed rate assets and liabilities respectively. Rate sensitive assets and liabilities are those
whose income or cost will change over some planning period if interest rates change and fixed
rate accounts will not. Any gains or losses to both banks should now be limited because both
wind up with equal amounts of rate sensitive assets and liabilities after including the effects of
the off balance sheet swap. Any profit changes due to the swap should be at least roughly offset
by offsetting changes in costs and rates of return on the balance sheet.
Credit risk exposure on a swap is less than on a loan since no principal is involved and only net
interest payments are at risk but credit risk is still present. The agent bank may guarantee swap
payments for a fee.
b. Currency Swaps
Currency swaps may be used to hedge mismatches in the currency of a FI’s assets and liabilities
or other commitments. As of June 2013 the notional principal of currency swap contracts
outstanding (adjusted for double counting) was $24.6 trillion. Note that most currency swaps do
involve swapping principal.
Fixed for fixed currency swaps involve a swap of principal and interest between two parties at a
fixed rate of exchange.
Fixed for floating currency swaps can be used to hedge both currency and interest rate
exposure simultaneously.
Teaching Tip: For example, a U.S. firm might have a British subsidiary that is earning pounds.
Suppose the subsidiary is not well known and cannot procure pound financing at an acceptable
cost, so the parent arranges variable rate dollar loans. The U.S. parent is now at risk if the pound
declines because a depreciating pound will make repaying the dollar loans more expensive.
Moreover, the loans are variable rate and cannot be fully hedged with forward contracts because
of the changing outflow amounts. The parent may arrange a swap with a counterparty where the
British subsidiary agrees to pay a fixed rate of interest (and principal when due) in pound sterling
in exchange for receiving a dollar denominated variable rate of interest (and principal).
c. Credit Swaps
BIS data indicates that credit swaps grew rapidly before the financial crisis and in 2013 there was
an estimated $21 trillion in notional principal on credit default swaps or CDS for short. This
number has been declining from its peak at $62 trillion in 2007. Losses on mortgage related
CDS written by Lehman Brothers and AIG led to the insolvency of these firms. Central clearing
houses have now been created for both Europe and the U.S. The major problem with the CDS
market was the lack of collateral and capital to back the promise to pay in the event of a default.
Clearinghouses can reduce or eliminate counterparty risk by requiring margin sufficient to back
the net value of the contract. These contracts are also employing more standardized terms.
There are two types of CDS. In a Total Return CDS, one party pays either a fixed or a variable
rate of interest to the seller and the counterparty makes floating rate payments representing the
total return (interest and principal value changes) on an underlying credit instrument. Values of
the total return CDS respond to more than changes in underlying default risk. In a Pure CDS the
protection buyer will make a fixed periodic payment to the protection seller and the protection
seller will pay the protection buyer if a credit event occurs.1 If the CDS is cash settled the
protection seller will pay the buyer the drop in price of the reference entity credit. If the CDS is
physical settled the buyer delivers the underlying bond or loan, and the seller pays the par value
of the security. Since no economic tie is required between the protection buyer and the reference
entity credit the notional principal outstanding on CDS can be far larger than the underlying
credit. Protection sellers can generate premium income with only a minimal upfront capital
requirement if the seller has a strong credit rating. This leads to the possibility of the creation of
an excessive amount of CDS. The top sellers of CDS have been hedge funds seeking additional
income, although insurers have been net sellers as well. If either the protection seller’s credit
standing or the reference entity’s credit rating drops, the buyer may require more collateral which
can pressure sellers financially. In early 2008 during the financial crisis the costs of this type
insurance rose dramatically. For instance, the cost to insure against a Citigroup debt issue default
increased from $9,700 in June 07 to $72,000 in January 2008 to $190,000 in March 2008,
reflecting the greater probability of default (source follows).2
1 The ‘credit event’ is typically default. For more information see the CBOT website file titled
“CDR Liquid 50 TM NAIG Index Futures FAQs.”
2 For more information see, “Swap Skirmish: Risks Hidden, Says Hedge Fund Citigroup, Wachovia Face Lawsuits
Involving Credit Derivatives,” by Susan Pulliam, Serena Ng & Tom Mcginty, The Wall Street Journal Online,
March 4, 2008; Page C1 and “New Spasm Jolts Credit Markets: Bankers Rattled As Turmoil Returns To
Short-Term Loans,” by Liz Rappaport, Joellen Perry And Deborah Lynn Blumberg, The Wall Street Journal
Online, March 6, 2008; Page A1.
Credit swaps allow a loan originator to shift the risk of a loan default to a swap seller. This may
allow more credit formation and generate faster economic growth, but it may also lead to an
erosion of underwriting standards. This undoubtedly occurred prior to the financial crisis of
2007-2008 and was a significant cause of the problems that ensued in mortgages.
d. Swap Markets
Swap dealers greatly facilitate the market for swaps. Large commercial banks and investment
banks are the primary swap dealers. Swap dealers usually guarantee payments on both sides of
the swap (for a fee). Dealers book their own swaps and keep a ‘swap book’ to facilitate
management of their net payment obligations. Regulators have worried that the swap market is
largely unregulated and some of the specific terms of swap agreements may not be publicly
available. Since the swap market involves U.S. banks, swap market activities are indirectly
regulated through the normal bank regulatory process. The Basle accord also specifies capital
requirements to offset the risks associated with swaps. As a result of the financial crisis swaps
will be more regulated. Although details are not available as of this writing it is likely that credit
default swaps will have either collateral requirements and/or be required to clear on an exchange.
6. Caps, Floors and Collars
Caps, floors and collars are options on interest rates. The majority of these contracts have
between 1 and 5 year maturities, although some have longer expirations.
Cap: A cap is an OTC call option on interest rates. Conceptually, it may also be thought of as
a put option on bond prices. If interest rates rise above a specified minimum (the strike
“price” or “cap rate”), the seller of the cap pays the buyer the difference between the market
interest rate and the strike interest rate times the notional value. Settlement (payment) dates
may be at the end of contract, annually, or at other times negotiated by the parties.
Floor: A floor is an OTC put option on interest rates. Conceptually, it may also be thought of
as a call option on bond prices. If interest rates fall below a specified minimum (the strike
“price” or “floor rate”), the seller of the floor pays the buyer the difference between the strike
and the market interest rate times the notional value.
Collar: A collar is a simultaneous position in a cap and a floor. If a FI is at risk from rising
(falling) interest rates they may wish to buy a cap (floor). To offset some of the cost of
purchasing the cap (floor) the FI may simultaneously sell a floor (cap).