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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.

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terms to be defined
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
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
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?








present value
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 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
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
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
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
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
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
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
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
“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