We cannot observe the term structure directly, but we can observe the market prices of instruments whose price depends on the term structure and thus estimate the term structure. A good source of information regarding the term structure is the government bond market, where usually a lot of liquid securities are traded whose prices depend solely on the term structure.
Suppose there are n bonds traded whose gross (or dirty) prices are denoted by . There are m dates when at least one bond's owners receive a payment. These payments are due in years time respectively where . The matrix C contains the cash flows of the bonds. We model bond prices as the sum of the present value of the bond's cash flow and a normally distributed error term:
Here d is the vector containing the discount factors and is a vector containing the error terms. The observed market price of a bond can differ from the present value of the cash flow for two reasons: there might be a measurement error...