Option markets

Exchange-traded and over-the-counter options
Options are traded both on organized exchanges and over-the-counter. The two
modes of trading are quite different and lead to important differences in market
conventions. The over-the-counter currency and interest rate option markets have
become much more liquid in recent years. Many option market participants prefer
the over-the-counter markets because of the ease with which option contracts tailored
to a particular need can be acquired. The exchanges attract market participants who
prefer or are required to minimize the credit risk of derivatives transactions, or who
are required to transact in markets with publicly posted prices.
Most money-center commercial banks and many securities firms quote over-thecounter
currency, interest rate, equity and commodity option prices to customers. A
smaller number participates in the interbank core of over-the-counter option trading,
making two-way prices to one another. The Bank for International Settlements (BIS)
compiles data on the size and liquidity of the derivatives markets from national
surveys of dealers and exchanges. The most recent survey, for 1995, reveals that over-the-counter markets dominate trading in foreign exchange derivatives and a
substantial portion of the interest rate, equity, and commodity derivatives markets.
We can summarize the key differences between exchange-traded and over-thecounter
option contracts as follows:
Ω Exchange-traded options have standard contract sizes, while over-the-counter
options may have any notional underlying amount.
Ω Most exchange-traded options are written on futures contracts traded on the
same exchange. Their expiration dates do not necessarily coincide with those of
the futures contracts, but are generally fixed dates, say, the third Wednesday of
the month, so that prices on successive days pertain to options of decreasing
maturity. Over-the-counter options, in contrast, may have any maturity date.
Ω Exchange-traded option contracts have fixed exercise prices. As the spot price
changes, such an option contract may switch from out-of-the-money to in-themoney,
or become deeper or less deep in- or out-of-the-money. It is rarely exactly
at-the-money. Thus prices on succesive days pertain to options with different
moneyness.
Ω Mostly American options are traded on the exchanges, while primarily European
options, which are simpler to evaluate, are traded over-the-counter.
Prices of exchange traded options are expressed in currency units. The lumpiness
of the tick size is not a major issue with futures prices, but can be quite important
for option prices, particularly prices of deep out-of-the-money options with prices
close to zero. The price of such an option, if rounded off to the nearest basis point
or 1
32 may be zero, close to half, or close to double its true market value. This in turn
can violate no-arbitrage conditions on option prices. For example, if two options with
adjacent exercise prices both have the same price, the convexity requirement is
violated. It can also lead to absurdly high or low, or even undefined, implied volatilities
and greeks.
In spite of their flexibility, there is a good deal of standardization of over-thecounter
option contracts, particularly with respect to maturity and exercise prices:
Ω The typical maturities correspond to those of forwards: overnight, one week, one,
two, three, six, and nine months, and one year. Interest rate options tend to have
longer maturities, with five- or ten-year common. A fresh option for standard
maturities can be purchased daily, so a series of prices on successive days of
options of like maturity can be constructed.
Ω Many over-the-counter options are initiated at-the-money forward, meaning
their exercise prices are set equal to the current forward rate, or have fixed deltas,
so a series of prices on successive days of options of like moneyness can be
constructed.
Fixed income options
The prices, payoffs, and exercise prices of interest rate options can be expressed in
terms of bond prices or interest rates, and the convention differs for different
instruments. The terms and conditions of all exchange-traded interest rate options
and some over-the-counter interest rate options are expressed as prices rather than
rates. The terms and conditions of certain types of over-the-counter interest rate
options are expressed as rates. A call expressed in terms of interest rates is identical
to a put expressed in terms of prices.

Caplets and floorlets are over-the-counter calls and puts on interbank deposit
rates. The exercise price, called the cap rate or floor rate, is expressed as an interest
rates rather than a security price. The payoff is thus a number of basis points rather
than a currency amount.
Ω In the case of a caplet, the payoff is equal to the cap rate minus the prevailing
rate on the maturity date of the caplet, or zero, which ever is larger. For example,
a three-month caplet on six-month US dollar Libor with a cap rate of 5.00% has
a payoff of 50 basis points if the six-month Libor rate six months hence ends up
at 5.50%, and a payoff of zero if the six-month Libor rate ends up at 4.50%
Ω In the case of a floorlet, the payoff is equal to the prevailing rate on the maturity
date of the cap minus the floor rate, or zero, which ever is larger. For example, a
three-month floorlet on six-month US dollar Libor with a floor rate of 5.00% has
a payoff of 50 basis points if the six-month Libor rate six months hence ends up
at 4.50%, and a payoff of zero if the six-month Libor rate ends up at 5.50%
Figure 1.8 compares the payoffs of caplets and floorlets with that of a FRA.
4.6 4.8 5 5.2 5.4
ST
40
20
0
20
40
payoff bp
payoff on FRA
payoff on caplet
payoff on floorlet
Figure 1.8 FRAs, caps and floors.
A caplet or a floorlet also specifies a notional principal amount. The obligation of
the writer to the option owner is equal to the notional principal amount times the
payoff times the term of the underlying interest rate. For example, for a caplet or
floorlet on six-month Libor with a payoff of 50 basis points and a notional principal
amount of USD1 000 000, the obligation of the option writer to the owner is
USD0.0050 · 1
2 · 1 000 000ó2500.
To see the equivalence between a caplet and a put on a bond price, consider a
caplet on six-month Libor struck at 5%. This is equivalent to a put option on a sixmonth
zero coupon security with an exercise price of 97.50% of par. Similarly. A
floor rate of 5% would be equivalent to a call on a six-month zero coupon security
with an exercise price of 97.50.
A contract containing a series of caplets or floorlets with increasing maturities is
called a cap or floor. A collar is a combination of a long cap and a short floor. It
protects the owner against rising short-term rates at a lower cost than a cap, since

the premium is reduced by approximately the value of the short floor, but limits the
extent to which he benefits from falling short-term rates.
Swaptions are options on interest rate swaps. The exercise prices of swaptions,
like those of caps and floors, are expressed as interest rates. Every swaption obliges
the writer to enter into a swap at the initiative of the swaption owner. The owner will
exercise the swaption by initiating the swap if the swap rate at the maturity of the
swaption is in his favor. A receiver swaption gives the owner the right to initiate a
swap in which he receives the fixed rate, while a payer swaption gives the owner the
right to initiate a swap in which he pays the fixed rate.
There are two maturities involved in any fixed-income option, the maturity of the
option and the maturity of the underlying instrument. To avoid confusion, traders in
the cap, floor and swaption markets will describe, say, a six-month option on a twoyear
swap as a ‘six-month into two year’ swaption, since the six-month option is
exercised ‘into’ a two-year swap (if exercised).
There are highly liquid over-the-counter and futures options on actively traded
government bond and bond futures of industrialized countries. There are also liquid
markets in over-the-counter options on Brady bonds.