Term structure: zero rates and discount factors

In short

• Interest rates have a term structure: a different rate for each maturity. The same applies to credit spreads, implied volatility and, with two curves, FX.
• A zero rate (spot rate) $z_i$ is the yield on a single cash flow at time i. A one-period bond's YTM equals $z_1$.
• Bootstrapping solves for zero rates one maturity at a time, using the zero rates already found to discount earlier coupons.
• Discount factor: $DF_i = 1/(1+z_i)^i$, the price today of one unit of currency at time i.
• An asset with a known future value must trade at its PV; if it does not, borrow-and-buy (or sell-and-lend) earns a riskless profit.