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Applications in Finance by Ramaprasad Bhar_12

Tham khảo tài liệu 'applications in finance by ramaprasad bhar_12', tài chính - ngân hàng, ngân hàng - tín dụng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 262 Stochastic Filtering with Applications in Finance Hence the estimation techniques available such als Stud MCL are applicable as both techniques exploit the fact that the system can be specified in a state space form. 10.2.2 Exogenous Variables In addition if additional exogenous variables difeufc ht to affect the volatility then these can be included. For instance Christiansen 2005 employed a bi-variate GARCH model to demonstrate that the volatility of the yield term spread i.e. the difference between the yield of a short term bond and a long term bond the volatility of short-term interest rates were correlated. Taking this notion further the log-variance of the yield term spread as an exogenous variable in the log-variance equation of the short rate. The term spread can be included in the dynamics of the logvariance as follows ht m l-j j -1j t 10.7 ht rr l-j j tvtd -1j L fi tqh t. 10.8 where Sf is the yield term spread at time t defined abocl eọaptures its impact on the volatility of the short-term interest rate process and L is the lag operator. Alternatively some studies have considered the impact of US Federal Reserve announcements on short-term interest rates as the yields on short-term bonds tend to closely track the Fed Funds rate. Das 2002 considers the effect of the Federal Open Market Committee FOMC meetings on the jump probability of short rates where an increase in jump probability corresponds to an increase in the volatility of the short rate. The findings suggest that the effect of 2-day FOMC meetings increased the probability of jumps occurring. Using a similar approach we incorporate a dummy variable for the FOMC meetings to determine whether there is an impact on volatility. In this case the value is 1 if there is an FOMC meeting in the preceding period and zero otherwise. This is incorporated in the SV models as follows ht m 1 -j 4-j tvtk ftỷh t 10.9 Stochastic Volatility Model and Non-Linear Filtering 263 ht rr 1 -j hf.t k ftỷh tqh t-v 10.10