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Applications in Finance by Ramaprasad Bhar_2

Tham khảo tài liệu 'applications in finance by ramaprasad bhar_2', tài chính - ngân hàng, ngân hàng - tín dụng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 32 Stochastic Filtering with Applications in Finance where De t t 1 represents the ex ante real interest rate differential from time t tot 01 seen at time tD t t 1 is the ex post real interest rate differential seen at timteol. Thus D t t D1 r t to 1Ũ r tpt 1 _1 . 1 1 .1 1 2.20 Eữ.tott e0t E eOt t 3 Here E t t 1 is the cross country differential in inflation forecast errors observed at 01. If we assume that the ex ante real interest rate differential follow an autoregressive process of order p then the following state space model results D t t 1 De t t 1 E t t 2.21 De t 1 t 2 f L .ơ t t 1 u t 2.22 with f L f ff 2I . f pLp1. In the state space terminology 2.21 is the measurement equation and 2.22 is state transition equation. Obviously estimation of such a model can be achieved by Linear Kalman Filter described in chapter 1. Cavaglia 1992 applies standard time series technique to arrive at the order p of the autoregressive process and assumes that the covariance matrix is time homogeneous. Data used in Cavaglia study consist of one-month Euro deposit rate for the US Germany Switzerland and Holland covering the period 1973 to 1979. Nominal interest rates were deflated by domestic inflation rates computed from the consumer price index reported by the IMF. The parameter estimates were carried out by likelihood maximization as discussed in chapter 1 Additional computational details could be obtained from Cavaglia 1992 . Table 2.4 gives the estimation results for the four countries and both the US and Germany were considers as the reference countries to compute the interest rate differentials. The selected models for the ex ante real interest differentials are all mean zero stationary processes. This is evidence in support of theoretical models of economic interdependence which imply a tendency towards real rate equality. Deviations from real rate equality are short-lived. The models presented in Table 2.4 can be utilized to generate forecasts of expected short-term real