Multiple bonds with different maturities

Suppose that you have two pure discount bonds outstanding, one with a one-year maturity and the other with a two-year maturity.

• two years from now you have an option to buy back the assets from the two-year bondholders
• to have that option you must pay off the one-year bondholders one year from now (i.e., you must exercise your option to buy back the assets from the one-year bondholders at the face value of the one-year debt)
• the one-year debt, then, is like an option on an option
• what do we call that?

Coupon Bonds

Suppose that we only have one debt issue outstanding, but that debt issue promises periodic coupon payments plus a return of principal at maturity. How would we characterize the coupon debt?