Interest Rate Term Structures

Interest rate curves are constructed from the prices of bonds traded in the market. In order to construct the spot rate curve (also called spot rate term structure for term structure, for short), for example, the yields of zero bonds for all possible maturities are required. Observing an entire array of conditions in order to be consistent with the assumption of an arbitrage-free market, such an interest rate curve can be determined from market data characterizing traded interest rate instruments. Such market data are for instance prices of traded bonds (not necessarily zero bonds), spot rates, par rates, swap rates, etc. All of these variables can be traced back to a single common nucleus. If the market is arbitrage-free (and assuming the same credit-worthiness for all cash flows involved) then for every value date t and maturity date T there exists a unique discount factor BR(t, T). If all possible discount factors are known, then the present value of every instrument or portfolio consisting of cash flows can be determined. Thus, the spot rate curve R(t, T) (which is nothing other than the yields of the discount factors BR(t, T)) has to be constructed in such a way that the observed market prices of interest rate instruments can be reproduced by discounting the future cash flows of the instruments using BR(t, T).