Semi-Closed-Form Pricing of Vulnerable Geometric Asian Options Under a Three-Factor Stochastic Volatility Jump-Diffusion Model with Stochastic Interest Rates
This paper develops a semi-closed-form pricing framework for vulnerable geometric Asian options under a three-factor stochastic volatility jump-diffusion model with stochastic interest rates. To the best of our knowledge, this is the new framework to simultaneously accommodate common and idiosyncratic volatility, co-jumps, stochastic rates, and counterparty default risk in a 2D-FFT setting. The theoretical contribution is threefold: (i) a fully flexible correlation structure among asset returns, volatility factors, and the short rate; (ii) a default intensity jump component correlated with asset jumps; and (iii) a two-dimensional fast Fourier transform (2D-FFT) algorithm that computes prices and all Greeks in a single execution. Numerical results demonstrate speedup factors of 22.6 to 114.2 over Monte Carlo simulation at comparable accuracy (APE below 0.02%), with near-constant time scaling for portfolios of up to 4096 options. Degeneracy tests confirm the framework correctly recovers known closed-form solutions and published benchmarks. The proposed method provides a computationally efficient pricing tool for real-time risk management of credit-risk-embedded derivatives.
With the rapid advancement of artificial intelligence technologies in the era of big data, time series forecasting has become indispensable in critical fields such as environmental monitoring and financial market analysis. However, the existing forecasting models often encounter…
Machine learning technologies are increasingly embedded in financial decision-making processes, yet their influence on investor behavior and market efficiency remains insufficiently understood. This study investigates how machine learning-assisted investment decisions affect inve…
Task decomposition is a fundamental challenge in multi-agent collaborative maintenance systems, where unstructured natural language instructions must be precisely translated into logically coherent, executable sub-task sequences. This paper formulates task decomposition as a cons…
In this descriptive scoping review, we assessed how Bayesian network structures are built and learned in applied work by screening 5993 recent papers (2020–2025) whose abstracts mention “Bayesian (belief) network” and deeming 3661 relevant. Among these relevant papers, expert kno…
Combinatorial optimization is a key component in critical decision problems such as routing, scheduling, network design, and graph optimization. Although combinatorial optimization methods, including exact algorithms, approximation methods, constraint programming, mixed integer p…
Longitudinal data, characterized by repeated measurements on the same subjects over time, are ubiquitous in biomedical sciences, economics, social sciences, and engineering. Analyzing such data presents unique statistical and computational challenges, including within-subject cor…