Nonlinear Mixed Effects Model And Its Application Of The Financial Risk

A core problem of financial market research is the volatility, volatility models are widely used in various financial assets such as stocks, foreign exchange, interest rates in the modeling, so the research of volatility model to the application of financial has important significance. Volatility modeling is one of the core problems in finance, and multivariate volatility model and its statistical inference is one of the difficulties, also received wide attention. Based on state space model, this paper studies statistical inference problem of multivariable stochastic volatility model, including parameters estimation and volatility forecast.For parameter estimation, using the monte carlo maximum likelihood method. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. Using the maximum likelihood estimation method to estimate the unknown parameters of the Gauss part, the parameters are considered as the parameters of the stochastic volatility model. Because Linear state-space model for multidimensional stochastic volatility model transformed is multi-dimensional, but the parameters is more and difficult to estimate, In this paper, the model parameters are modeled by a hierarchical model, and the model is transformed into a mixed effects state space model, Then the EM algorithm is used to get the expression of the EM algorithm, and then estimate the unknown parameters of the Gauss part by numerical simulation.For volatility forecast,under the condition of the individual random effects is unknown, via the plain mixture Kalman filter, mixture Kalman filter with Metropolis move and mixture Kalman filter with kernel smoothing of the three filtering algorithm based on sequential monte carlo simulation technique, to estimate the state, but also estimate the parameters of the individual.Finally has carried on the numerical analysis of the above statistical inference method. The simulation of parameter estimation algorithm results show that the EM algorithm is a good way to estimate parameters, and the more observation data, the more accurate of parameter estimation; The simulation of state estimation results show that the plain mixture Kalman filter algorithm shortest but estimated effect is the worst, mixture Kalman filter with Metropolis move works best but time is too long, and mixture Kalman filter with kernel smoothing is very good and time is short, Comprehensive consideration is optimal. Finally, the stochastic volatility model is applied to the prediction of stock volatility, and Verified the effectiveness of the model.