Quantitative Finance

17Models for the Bond Market

17.1 Introduction and Notations

This chapter serves as an introduction to bond market models. The main instrument studied is a bond price which is entirely different from stock price. A bond is an investment product that is issued by corporate and governmental entities to raise capital to finance and expand their projects and operations. The bond market is where debt securities are issued and traded. The differences in the bond and stock market lie in the manner in which the different products are sold and the risk involved in dealing with both markets. For instance, the stock market has stock exchanges where stocks are bought and sold. However, the bond market does not have a central trading place for bonds; rather bonds are sold mainly over the counter (OTC). The other difference between the stock and bond market is the risk involved in investing in both. Investing in bond market is usually less risky than investing in a stock market because the bond market is not as volatile as the stock market is. Throughout this chapter the notional principal value is taken as 1 (unit). The notional principal amount is the predetermined dollar amounts on which the exchanged interest payments are based. The notional principal never changes hands in the transaction, which is why it is considered notional, or theoretical.

17.2 Notations

We begin this section with some definitions and notations that would be used throughout this chapter.

Short Rate

Let be ...