The estimation problem

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...