In this second part of the book we move one step forward in the understanding of fixed income instruments. In particular, we introduce the notion of no arbitrage, and the basics of term structure modeling. To advance the topic, let’s consider the following example.
Consider a trader in a prominent investment bank. By using a bootstrap methodology or any of the other methodologies discussed in Chapter 2, the trader has estimated the current discount function Z (0, T). Recall that Z (0, T) gives the value today (0) of one dollar at time T.
If a client asks the trader to quote the price of 10%, 5-year, T-bond, the trader has all the information needed. The price can be computed from
Suppose now that the client asks the trader to quote the price of a 10%, 5-year, callable T-bond, that is, such that the Treasury has the option to buy it back at par at some date in the future.
Methodology 1 (Naive)
Naively we can follow this reasoning: