Key Technique of Almost Exact Simulation for Non-affine Heston Model

In order to sample asset price more accurately under the non-affine Heston model in the situation where the Feller condition was unsatisfied, we proposed the key technique of almost exact simulation for non-affine Heston model, by fusing the approximate analytic solution of conditional variance characteristic function, the second-order Newton's method and interpolation method. Numerical results on four representative benchmarks show that our newly proposed simulation scheme has both good convergence and accuracy, which are much better than those of the Itô-Taylor schemes. Especially, our scheme performs well in the case where the Feller condition is extremely unsatisfied, while the alternatives don't work.