Thứ ba, các nhà đầu tư và quản lý rủi ro cần phải biết sự biến động của danh mục đầu tư thu nhập cố định. Nếu, ví dụ, một người quản lý rủi ro kết luận rằng sự biến động của lãi suất 100 điểm cơ bản mỗi năm và tính toán rằng giá trị của một số thay đổi danh mục đầu tư $ đô la cho mỗi điểm cơ bản, | 10 The Short-Rate Process and the Shape of the Term Structure Given the initial term structure and assumptions about the true interest rate process for the short-term rate Chapter 9 showed how to derive the risk-neutral process used to determine arbitrage prices for all fixed income securities. Models that follow this approach and take the initial term structure as given are called arbitrage-free models of the term structure. Another approach to be described in this and subsequent chapters is to derive the risk-neutral process from assumptions about the true interest rate process and about the risk premium demanded by the market for bearing interest rate risk. Models that follow this approach do not necessarily match the initial term structure and are called equilibrium models. The benefits and weaknesses of each class of models are discussed throughout Chapters 11 to 13. This chapter describes how assumptions about the true interest rate process and about the risk premium determine the level and shape of the term structure. For equilibrium models an understanding of the relationships between the model assumptions and the shape of the term structure is important in order to make reasonable assumptions in the first place. For arbitrage-free models an understanding of these relationships reveals the assumptions implied by the market through the observed term structure. Many economists might find this chapter remarkably narrow. An economist asked about the shape of the term structure would undoubtedly make reference to macroeconomic factors such as the marginal productivity of capital the propensity to save and expected inflation. The more modest goal of this chapter is to connect the dynamics of the short-term rate of interest and the risk premium with the shape of the term structure. While this goal does fall short of answers that an economist might provide 193 194 THE SHORT-RATE PROCESS AND THE SHAPE OF THE TERM STRUCTURE it is more ambitious than the derivation of
