2020/03/13 by Fan Jiang, Jiang, Fan, Xin Zang +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Finance (q-fin.CP) #FOS: Economics and business #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2003.06218
openalex publication_date 2020/03/13 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In this paper, enlightened by the asymptotic expansion methodology developed\nby Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for\nthe transition densities of the stochastic differential equations (SDEs) driven\nby the gamma processes, a special type of Levy processes. After representing\nthe transition density as a conditional expectation of Dirac delta function\nacting on the solution of the related SDE, the key technical method for\ncalculating the expectation of multiple stochastic integrals conditional on the\ngamma process is presented. To numerically test the efficiency of our method,\nwe examine the pure jump Ornstein--Uhlenbeck (OU) model and its extensions to\ntwo jump-diffusion models. For each model, the maximum relative error between\nour approximated transition density and the benchmark density obtained by the\ninverse Fourier transform of the characteristic function is sufficiently small,\nwhich shows the efficiency of our approximated method.\n