Some Terminology

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 2 3 $8 $8 $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:

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

Some Terminology