Density Approximation of Affine Jump Diffusions via Closed-Form Moment Matching

2025-04-09

AI Summary

This paper addresses the challenge of analytically characterizing the conditional and unconditional density functions for affine jump-diffusion models with state-independent jump intensities. We propose a novel density approximation method based on closed-form moment recursion and generalized moment matching. For the first time, we derive explicit recursive formulas for all orders of conditional and unconditional moments of such processes and construct a density approximation that admits an analytical expression—up to the normalization constant. Compared to conventional Monte Carlo simulation, our method achieves comparable accuracy in option pricing and path simulation while improving computational efficiency by an order of magnitude. This advancement significantly extends the practical applicability of affine jump-diffusion models in financial derivative pricing and high-efficiency stochastic simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• User Modeling, Personalization and Recommendation: User model development and evaluation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form density approximations (up to a normalization constant) via moment matching for both conditional and unconditional distributions. Our framework enables important financial applications, including efficient option pricing and exact simulation for affine jump diffusions. Numerical experiments demonstrate the method's superior computational efficiency compared to existing simulation techniques, while preserving numerical precision.

Problem

• Develop recursive method for affine jump diffusions moments
• Construct closed-form density approximations via moment matching
• Enable efficient option pricing and exact simulation

Innovation

• Recursive closed-form moment solutions
• Moment matching for density approximations
• Efficient option pricing and simulation