Research on Mathematical Model of Portfolio Risk Measurement Based on Likelihood Ratio

In this paper, a real-time monitoring method of portfolio risk measurement based on likelihood ratio is proposed through the research paradigm of intelligent simulation analysis. The value of simulation data is mined with the idea of green simulation, and a theoretical model is built to realize a real-time monitoring method of portfolio risk measurement with a fixed length of time, that is, the portfolio risk measurement can always be obtained after a certain period of time when the market state is given at the current moment. Using large loss probability as a measure of investment risk, the simulation path and the corresponding portfolio loss of each path are obtained according to nested Monte Carlo simulation and likelihood ratio method, and the logistic regression equation is established to calculate the equation coefficient using the maximum likelihood estimation method. The convergence and convergence rate of logistic regression model are proved. When the sample path of the inner and outer layers tends to infinity at the same time, the estimated coefficient of logistic regression equation will converge to the true value, and the convergence rate of the outer layer path is the square times of the inner layer. Numerical experiments are carried out on the theoretical model, and the experimental results show that the model has a good effect on the whole, and can effectively predict the risk of the investment portfolio in the initial period of time. Further, this paper uses the method of updating parameters to rebuild the simulation model to solve the problem that the effect of the model becomes worse and worse with the increase of time. In addition, the robustness of the proposed method is proved by multiple test sets and sensitivity estimation. Finally, empirical research was carried out using actual data to collect the option data of Yahoo Finance to build a portfolio, and the corresponding stock data of each option was monitored. The experimental results showed that even if the underlying assets changed slightly, the risk of the portfolio still changed greatly. Therefore, this method can guide managers to monitor portfolio risks in real time, which is of great significance for actual financial risk management.