II. Options
A. Puts, Calls, and All That: Definitions
1. Like futures, options are agreements between two parties, a seller (option writer) and
a buyer (option holder).
2. Option writers incur obligations, while option holders obtain rights.
3. There are two basic options, calls (the right to buy) and puts (the right to sell).
4. A call option has a predetermined price (the strike price) and a specific date.
a) The writer of the call option must sell the shares if and when the holder
chooses to use the call option, but the holder is not obligated to buy the shares.
b) The holder will buy (exercise the option) only if doing so is beneficial.
c) The holder could also sell the option to someone else at a profit.
B. Whenever the price of the stock is above the strike price of the call option, the option is
“in the money”. (If the prices are equal it is “at the money” and if the price is less than
the stock price it is “out of the money”.)
1. A put option gives the holder the right but not the obligation to sell the underlying
asset at a predetermined price on or before a fixed date.
a) The writer of the option is obliged to buy the shares if the holder chooses to
exercise the option.
b) Puts are “in the money” when the option’s strike price is above the market
price of the stock; they are “out of the money” when the strike price is below
the market price, and “at the money” when the two prices are equal
2. Many options are standardized and traded on exchanges just like futures contracts,
and the mechanics of trading are the same.
3. There is a clearing corporation, but only writers of options are required to post
margin.
a) There are two types of options: American options can be exercised on any
date from the time they are written until the day they expire; European options
can only be used on the day they expire
b) The vast majority of options traded in the United States are American.
C. Using Options
1. Options transfer risk from the buyer to the seller so they can be used for both hedging
and speculation.
2. When used for hedging, a call option ensures that the cost of buying the asset will not
rise and a put option ensures that the price at which the asset can be sold will not go
down.
a) Car insurance is like an American call option, sold by the insurance company
to the car’s owner.
3. How options are used for speculation: if you believed that interest rates were going to
fall, you could bet on this by buying a bond (expensive), buying a futures contract
(cheap but risky), or by buying a call option on a U.S. Treasury bond. If you are right,
its value will increase; if you are wrong all you lose is the price paid for the call
option.
4. Purchasing a put option allows an investor to speculate on a decrease in the price of
an asset.
5. Sellers of options are speculators or are insured against any loss that may arise
because they own the underlying asset (market makers).
6. Options are versatile and can be bought and sold in many combinations.
7. Options can be used to construct synthetic instruments that mimic the payoffs of
virtually any other financial instrument.
8. Options allow investors to bet that prices will be volatile.
D. Pricing Options: Intrinsic Value and the Option Premium
1. An option price is the sum of two parts: the value of the option if it is exercised (the
intrinsic value) and the fee paid for the option’s potential benefits (the time value of
the option).
2. As the volatility of the stock price rises, the time value of the option rises with it.
3. In general, calculating the price of an option and how it might change means
developing some rules for figuring out its intrinsic value and the time value of the
option.
4. Since the buyer is not obligated to exercise it, the intrinsic value of the option
depends only on what the holder receives if it is exercised.
5. The intrinsic value is the difference between the price of the underlying asset and the
strike price of the option, or the size of the payment, and it must be greater than or
equal to zero.
6. At expiration, the value of an option equals its intrinsic value, but prior to expiration
there is always the chance that the price will move.
7. The longer the time to expiration, the bigger the likely payoff when the option does
expire and thus the more valuable it is.
8. The likelihood that an option will pay off depends on the volatility of the price of the
underlying asset; the time value of the option increases with that volatility.
E. The Value of Options: Some Examples
1. At a given price of the underlying asset and time to expiration, the higher the strike
price of a call option, the lower its intrinsic value and the less expensive the option.
2. At a given price of the underlying asset and time to expiration, the higher the strike
price of a put option, the higher the intrinsic value and the more expensive the option.
3. The closer the strike price is to the current price of the underlying asset, the larger the
option’s time value.
4. Deep in-the-money options have lower time value. Because such an option is very
likely to expire “in the money,” buying one is like buying the underlying asset itself.
5. The longer the time to expiration at a given strike price, the higher the option price.
III.Swaps
A. Interest rate swaps are a type of derivative that allows government debt managers to keep
interest costs low while they manage revenues. Credit default swaps (CDSs) are a form of
insurance that allow a buyer to own a bond or mortgage without bearing its default risk.
B. Understanding Interest Rate Swaps
1. Interest rate swaps are agreements between two counterparties to exchange periodic
interest rate payments over some future period, based on an agreed-upon amount of
principal, called the notional principal.
2. Notional principal is called that because the principal is not borrowed, lent, or
exchanged; it is just the basis for the calculations involved.
3. In the simplest type of interest rate swap the parties exchange a variable rate for a
fixed rate.
C. Pricing and Using Interest Rate Swaps
1. The benchmark rate for a swap is the market interest rate on a U.S. Treasury bond of
the same maturity as the swap.
2. The swap rate is the rate to be paid by the fixed-rate buyer.
3. The difference between the benchmark rate and the swap rate is called the swap
spread, and is a measure of risk.
4. In recent years it has attracted substantial attention as a measure of the overall risk in
the economy (systematic risk); when it widens it signals that general economic
conditions are deteriorating.
5. Interest rate swaps are used by government debt managers and by those who seek to
reduce the risk generated by commercial activities (like banks that have fixed-rate
assets and variable-rate liabilities).
6. The primary risk in a swap is the risk that one of the parties will default.
7. Unlike futures or options, swaps are not traded on organized exchanges so they are
difficult to resell.
D. Credit Default Swaps
1. Credit default swaps (CDSs) is a credit derivative that allows lenders to ensure
themselves against the risk that a borrower will default.
2. The buyer of a CDS makes payments to the seller and the seller agrees to pay if an
underlying loan or security defaults.
3. CDS lasts several years and requires collateral be posted to protect against the
inability to pay either the buyer or seller.
4. CDSs contributed to the financial crisis in three ways
a) Fostering uncertainty about who bears the credit risk on a given loan or
security
b) Making the leading CDS sellers mutually vulnerable
c) Making it easier for sellers of insurance to assume and conceal risk
Appendix: Payoff Diagrams for Futures and Options
This appendix introduces payoff diagrams for options and futures contracts, and explains
how to use them. Combinations to customize risk are also illustrated in terms of
combining some of the figures presented.
Terms Introduced in Chapter 9
American option
arbitrage
call option
centralized counterparty (CCP)
credit-default swap (CDS)
derivatives
European option
fixed-rate payer
floating-rate payer
forward contract
futures contract
interest-rate swap
margin
notional principal
put option
strike price
swap
swap spread
time value of an option
Using FRED: Codes for Data in This Chapter
Data Series FRED Data Code
1‐year swap rate MSWP1
2‐year swap rate MSWP2
5‐year swap rate MSWP5
10‐year swap rate MSWP10
10‐year U.S. Treasury yield GS10
Central bank liquidity swaps held by Federal Reserve SWPT
CBOE Volatility Index: VIX VIXCLS
Lessons of Chapter 9
1. Derivatives transfer risk from one person or firm to another. They can be used in any
combination to unbundle risks and resell them.
2. Futures contracts are standardized contracts for the delivery of a specified quantity of a
commodity or financial instrument on a prearranged future date, at an agreed-upon price.
They are a bet on the movement in the price of the underlying asset on which they are
written, whether it is a commodity or a financial instrument.
a. Futures contracts are used both to decrease risk, which is called hedging, and to increase
risk, which is called speculating.
b. The futures clearing corporation, as the counterparty to all futures contracts, guarantees
the performance of both the buyer and the seller.
c. Participants in the futures market must establish a margin account with the clearing
corporation and make a deposit that insures that they will meet their obligations.
d. Futures prices are marked to market daily, as if the contracts were sold and repurchased
every day.
e. Since no payment is made when a futures contract is initiated, the transaction allows an
investor to create a large amount of leverage at a very low cost.
f. The prices of futures contracts are determined by arbitrage within the market for
immediate delivery of the underlying asset.
3. Options give the buyer (option holder) a right and the seller (option writer) an obligation to
buy or sell an underlying asset at a predetermined price on or before a fixed future date.
a. A call option gives the holder the right to buy the underlying asset.
b. A put option gives the holder the right to sell the underlying asset.
c. Options can be used both to reduce risk through hedging and to speculate.
d. The option price equals the sum of its intrinsic value, which is the value if the option is
exercised, and the time value of the option.
e. The intrinsic value depends on the strike price of the option and the price of the
underlying asset on which the option is written.
f. The time value of the option depends on the time to expiration and the volatility of the
price of the underlying asset.
4. Interest-rate swaps are agreements between two parties to exchange a fixed for a variable
interest rate payment over a future period.
a. The fixed-rate payer in a swap pays the U.S. Treasury bond rate plus a risk premium.
b. The flexible-rate payer in a swap normally pays the London Interbank Borrowing Rate
(LIBOR).
c. Interest-rate swaps are useful when a government, firm, or investment company can
borrow more cheaply at one maturity, but would prefer to borrow at a different maturity.
d. Swaps can be based on an agreed-upon exchange of any two future sequences of
payments.
5. Credit-default swaps (CDSs) are a form of insurance in which the buyer of the insurance
makes payments (like insurance premiums) to the seller, who in turn agrees to pay the buyer
if an underlying loan or security defaults.
a. A CDS agreement often lasts several years and requires that collateral be posted to
protect against the inability to pay of the seller or the buyer of insurance.
b. Because financial institutions do not report CDS sales and purchases, it is not clear who
bears credit risk on a given loan or security.
c. Because CDS are traded over the counter, even traders cannot identify others who take on
concentrated risks on one side of a trade.
6. Derivatives allow firms to arbitrarily divide up and rename risks and future payments,
rendering their actual names irrelevant.