مقاله سال ۲۰۱۷

As a measure of cost of capital and profit in modern financial market, interest rate is a top priority for any country. Interest rates have become the core content of the economic research not only for its nature of value measurement in bond market, but also for its importance in monetary policy transmission. Changes in interest rates generally reflect the tightness of the monetary policy of a country. In this way, interest rates significantly influence money supply, lending, stock market, and real economy in the end [1].

Earlier on, interest rates (prices of bonds) and prices of other financial properties are believed to follow random walk [2, 3]. Thus price changes are assumed to obey Gaussian distributions. However, recent researches prove that price changes follow a complex distribution with a more obvious peak and fatter tails than Gaussian’s [4, 5, 6]. It states in some economists’ and physicists’ research that interest rates fluctuation shows some complex properties, such as long range correlation or memory [7, 8, 9], fractals/multifractals [10, 11], and so on.

Long-range correlations appear in several kinds of equities in literature [12, 13, 14], but only a few of them focus on bond market. Backus and Zin (1993) [15]seem to be the first to consider the existence of long-range memories in interest rates. They use a fractional difference model to study the features of yields on US government bonds with modern asset pricing theory and find the evidence of long memory in the 3-month zero-coupon rate. Cajueiro and Tabak (2006) [10]test for long-range dependence in the term structure of London Interbank offered rates (LIBOR), which are considered to be the benchmark interest rates in European countries. They found significant evidence which shows that interest rates have a strong degree of long-range dependence and furthermore a multifractal nature. And they also suggest that the pricing of interest rates derivatives and fixed income portfolio management should take long memories into account.