Some Terminology
Lecture 3
Terms to Be Defined
Bond cash flows and present value
Options and interest rate options
(caps/floors)
Callable bond
Path dependent or path independent options
Credit risk
“On-the-run” securities
Bond terminology
Bonds typically pay periodic interest
payments called “coupons”

Annual coupon income is coupon rate times
face value
For simplicity, we will almost always use
annual coupons

In practice, bond coupons are usually paid in
semiannual installments
An example of a bond
A $100 face value bond has an annual
coupon of 8%. It expires in exactly 3 years.
What do the cash flows look like?
0
1
$8
2
$8
3
$8+$100
Present Value
Value of a bond (or any series of cash
flows) is determined by discounting the
cash flows by the appropriate interest rate
Key issue is determining the appropriate
interest rate (See lecture 4)
Options
Options provide the owner the right, but not
the obligation, to buy or sell an asset at a
fixed price
Call option is right to buy
 Put option is right to sell

The fixed price is called the exercise price
Options have an expiration or maturity date
Example of a call option
Today is April 1, Allison has the right to buy
MSFT at $70 per share from Bob on
December 31
Bob is obligated to sell MSFT to Allison at
$70 if she decides to “exercise” the option
Allison wants price to go up
Allison must pay Bob a “premium” to own
this call option
Callable Bonds
Look like other bonds

Schedule of specific coupons and principal
Give the issuer the discretion to retire the
debt early, prior to the scheduled maturity
Useful when interest rates decline

Reissue a new bond with lower interest expense
Investor may need to reinvest proceeds at
the current (lower) interest rate
Interest Rate Caps
Analogous to a call option on the interest rate
Provides a payoff to the buyer if a reference
interest rate rises above the cap level (or strike
rate)

Useful for a borrower concerned about rising
interest rates
Cap payments are related to some “notional
principal”
Some Details of a Cap
Unlike a call or put option, a cap has multiple
potential payoffs determined by a settlement
frequency and a maturity
At each settlement date, if the underlying index is
below the strike rate, no payments are exchanged
If the underlying index exceeds the strike rate, the
seller of the cap must pay:
(Index Rate - Strike Rate)  Notional Amount
 (Days in settlement period  360)
Interest Rate Floors
Analogous to a put on interest rates
Provides a payoff to the buyer if the
reference interest rate falls below the
floor level
 Useful
for an investor concerned about
falling interest rates
Path Dependent vs. Path
Independent Options
Valuation of interest rate caps only depends
on level of reference interest rate at
settlement

Caps are path independent
Sometimes a security’s value depends on
the path of interest rates

Mortgage prepayments are high the first time
interest rates fall
Credit Risk and Default
In most cases, we will assume risk-free cash flows

Discount rate is from US Treasuries
Default risk is uncertainty in payments of interest
or principal


Increases the required return
Present value is lower
Credit spread is extra amount of interest charged
above similar risk-free rate
“On-the-run” Securities
US Treasury has auctions for sale of new
securities
Most recently issued securities are most
liquid

Called on-the-run
Try to use on-the-run securities as much as
possible