2007/02/28 by Di Zhang, Zhang, Di, Roderick Melnik +1
Economics, Econometrics and Finance · #Banking stability, regulation, efficiency #Computational Engineering #Credit Risk and Financial Regulations #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Stochastic processes and financial applications #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.cs/0702166
openalex publication_date 2007/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with jump-diffusion. While the application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, it becomes computationally inefficient which severely restricts its applicability in many practically interesting cases. In this contribution, we focus on the development of efficient Monte-Carlo-based computational procedures for solving the FPT problem under the multivariate (and correlated) jump-diffusion processes. We also discuss the implementation of the developed Monte-Carlo-based technique for multivariate jump-diffusion processes driving by several compound Poisson shocks. Finally, we demonstrate the application of the developed methodologies for analyzing the default rates and default correlations of differently rated firms via historical data.