<p>In this paper, the problem of pricing bivariate options under a generalized stochastic volatility jump-diffusion portfolio model is investigated. Firstly, the jump element is incorporated into the multi-scale stochastic volatility model, and the partial differential equation satisfied by the price is deduced. Secondly, by using the operator decomposition technique and recovery rate expansion technique, the nonlinear equation is transformed into the linear part and Poisson equation part, and the system of coefficient equations is obtained. Thirdly, through the backtracking analysis of the exchangeability of the operator and the independence of the coefficients with some variables, the analytical solutions of the first-order coefficients concerning the zero-order coefficients are obtained. Finally, the analytical solutions of all second-order coefficients are obtained through function decomposition and item-by-item analysis, and the validity of all parameters is guaranteed. Compared with the previous studies of no jump term and first-order asymptotical solution, the joint jump term of this model is more in line with the characteristics of financial practice and the second-order asymptotical solution is more in line with the requirements of accurate pricing.</p>