Negative Real Interest Rates
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Negative Real Interest Rates
Negative Real Interest Rates
Negative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesrdiff. CF244AG. UK b Graduate School of Management, University of Auckland, Auckland, 1142, New Zealand c Business School, University of East Anglia, Chancellor’s Drive, Norwich. NR4 7TJ, UK đ Business School, University of Sydney, Codrington Street, Sydney, NSW, 2008, Australia • Business Schoo). U Negative Real Interest Ratesniversity of Newcastle. Callaghan. NSW. 2308, AustraliaStandard textbook general equilibrium term structure models such as that developed by Cox, IngeNegative Real Interest Rates
rsoll and Ross (1985b), do not accommodate negative real interest rates. Given this, the Cox, Ingersoll and Ross (1985b) “technological uncertainty vaNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesolatility and also allows for negative real interest rates. The Fokker-Planck (that is, the Chapman-Kolmogorov) equation is then used to determine the conditional moments of the instantaneous real rate of interest. These enable one to determine the mean and variance of the accumulated (that is, inte Negative Real Interest Ratesgrated) real rate of interest on a bank (or loan) account when interest accumulates at the instantaneous real rate of interest defined by the PearsonNegative Real Interest Rates
Type IV probability density. A pricing formula for pure discount bonds is also developed. Our empirical analysis of short dated Treasury'- bills showsNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest RatesV probability density.Key Words: Fokker-Planck equation; Mean reversion; Real interest rate; Pearson Type IV probability density.JEL classification; C61; C63; E43 1 * *1 The authors gratefully acknowledge the comments, criticisms and assistance of Emeritus Professor AlanHawkes of Swansea University Negative Real Interest Ratesand the referees in the development of this paper. All remaining errors andomissions are the sole responsibility of the authors.21IntroductionThe Cox,Negative Real Interest Rates
Ingersoll and Ross (1985b) model of the term structure of interest rates has been described as "... the premier textbook example of a continuous-timeNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesled that Cox, Ingersoll and Ross (1985b) formulate a quasi-supply side model of the economy based on the weak aggregation criteria of Rubinstein (1974) and where the optimising behaviour of a representative economic agent centres on a “technological uncertainty” variable that evolves in terms of a c Negative Real Interest Ratesontinuous time branching process.2 Bernoulli preferences are then invoked (0 determine the instantaneous prices of the Arrow securities for the economNegative Real Interest Rates
y and these in turn are used to form a portfolio of securities with an instantaneously certain real consumption pay-off. Adding the prices of the ArroNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Rates the real risk free rate of interest develops in terms of the well known Cox. Ingersoll and Ross (1985b, 391) “square root” (or branching) process and that because of this, the real risk free rate of interest can never be negative. Whilst early empirical assessments of the Cox, Ingersoll Ross (1985b Negative Real Interest Rates) term structure model were largely supportive, they were conducted before the onset of the Global Financial Crisis when the incidence of negative reaNegative Real Interest Rates
l interest rates was rare (Gibbons and Ramaswamy, 1993; Brown and Schaefer, 1994). This contrasts with the period following the Global Financial CrisiNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesrest rates were continuously negative in the United Kingdom over the period from 2009 until 2013. Other countries that have experienced negative real interest rates over all or part of this period2Otherwise known as a Feller (1951 a. 1951b) Diffusion.https://khothuvien.cori!3include Algeria, Argenti Negative Real Interest Ratesna, Bahrain, Belarus, China, Kuwait, Libya, Oman, Pakistan, Qatar, Russia and Venezuela to name but a few. Hence, given the increasing incidence of neNegative Real Interest Rates
gative real interest rates since the onset of the Global Financial Crisis and the difficulties the Cox, Ingersoll and Ross (1985b) term structure modeNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesobability density (Kendall and Stuart, 1977, 163-165). The Pearson Type IV is the limiting form of a skewed Student “r" probability density with mean reverting sample paths and time varying volatility and encompasses both the well known Uhlenbeck and Ornstein (1930) process and the scaled “t” proces Negative Real Interest Ratess of Praetz (1972, 1978) and Blattberg and Gonedes (1974) as particular cases. More important, however, is the fact that the Pearson Type IV density cNegative Real Interest Rates
an accommodate negative real interest rates.We begin our analysis in section 2 by following Cox, Ingersoll and Ross (1985b, 390-391) in considering anNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesate variable is then used to develop a set of Arrow securities that lead to a real interest rate process whose steady state (that is, unconditional) statistical properties are compatible with the Pearson Type IV probability density function. Section 3 then invokes the Fokker-Planck (that is, the Cha Negative Real Interest Ratespman-Kolmogorov) equation in conjunction with the stochastic differential equation implied by the Pearson Type IV probability density to determine theNegative Real Interest Rates
conditional moments of the instantaneous real risk free rate of interest. In section 4 we employ the steady state interpretation of the Fokker-PlanckNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Rates is strongly compatible with the way real interest rates evolve in practice. We then move on in section 5 to determine the mean and variance of the accumulated (that is, integrated) real rate of interest on a bank (or loan) account when interest accumulates at the instantaneous real4rates of interes Negative Real Interest Ratest characterised by the Pearson Type IV probability density. In section 6 we determine the price of a pure discount bond when the real rate of interestNegative Real Interest Rates
evolves in terms of the stochastic differential equation which defines the Pearson Type IV probability density. Section 7 concludes the paper and ideNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesb, 390) in considering an economy in which variations in real output hinge on a state variable, Y(t), which summarises the level of “technological uncertainty” in the economy? The development of the technological uncertainty variable is described by the stochastic differential equation?dY(í) =(a+bY( Negative Real Interest Ratest))dt + .mỉ + m;(- ^4^- Y(O)?.dz(r)-1Vbwhere a > 0, njj, m, and b < 0 are parameters, w captures the skewness in the probability density for Y(t) andNegative Real Interest Rates
dz(t) is a white noise process with a unit variance parameter (Hoel, Pon and Stone 1987, 142). This means that increments in technological uncertaintyNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesd by the technological uncertainty variable in the determination of the real rate of interest is to be found in Cox. Ingersoll and Ross (1985a, 364-368: 1985b, 390-391). Beyond this formal statement, however, Cox, Ingersoll and Ross (1985a, 1985b) have relatively little to say about the empirical me Negative Real Interest Ratesaning of the technological uncertainty variable. The context In which the technological uncertainty variable is introduced in the Cox, Ingersoll and RNegative Real Interest Rates
oss (1985a, 1985b) term structure model would suggest that it encapsulates factors such as the economy’s natural endowments, the enterprise, ingenuityNegative Real Interest Rates*Jing Chen", Diandian Mab, Xiaojong Song', Mark Tippett4'‘School of Mathematics. Cardiff University. Senghennydd Road. Car Negative Real Interest Ratesystem, the political independence of its monetary authorities and so on.4The specification of the state variable given here encompasses both positive and negative values. It therefore differs from the state variable employed for the technological uncertainty variable in the Cox, Ingersoll and Ross ( Negative Real Interest Rates1985b, 390) term structure model, which is based on a continuous time branching process. There are various interpretations of tlie branching process (Negative Real Interest Rates
Feller 1951a, 1951b) but all of them constrain tlie state variable to be non-negative and thus, they all differ from the state variable based on the PGọi ngay
Chat zalo
Facebook