An American-style lookback option pricing method based on the jump diffusion model and sentiment factors

With the rapid development of the financial market, the issue of option pricing has also attracted widespread attention. In order to solve the problem of American lookback option pricing, this paper improves the traditional finite element numerical algorithm by introducing the jump diffusion model and emotional factors, combined with the implicit time discrete method. At first, the American lookback option problem is modeled and transformed into a nonlinear parabolic problem suitable for finite element discrete. Then, discrete methods such as hidden BDF2, CNLF, and CNAB were used to solve the numerical problem. By introducing the O-U process model of stock sentiment and option sentiment, the accuracy of option pricing is further improved. Finally, the stability and convergence of the proposed method are verified by numerical experiments, and it has strong practical application potential.