2023/08/17 by Dennis Kristensen, Kristensen, Dennis, Young Jun Lee +3
Economics, Econometrics and Finance · #Computation (stat.CO) #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2308.09009
openalex publication_date 2023/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones in Kristensen and Mele (2011) to cover general Markov processes. We demonstrate that the class of expansions nests the transition density and option price expansions developed in Yang, Chen, and Wan (2019) and Wan and Yang (2021) as special cases, thereby connecting seemingly different ideas in a unified framework. We show how the general expansion can be implemented for fully general jump--diffusion models. We provide a new theory for the validity of the expansions which shows that series expansions are not guaranteed to converge as more terms are added in general. Thus, these methods should be used with caution. At the same time, the numerical studies in this paper demonstrate good performance of the proposed implementation in practice when a small number of terms are included.