Application of Stochastic Process Models and Numerical Methods in Financial Product Pricing

Abstract

Pricing of financial products has been one of the core issues in finance. Stochastic process models and numerical methods play a key role in financial product pricing. This paper aims to investigate the application of these methods in financial pricing, exploring the classical Black-Scholes model, stochastic volatility model and jump diffusion model, as well as numerical methods such as finite difference method, Monte Carlo simulation and volatility Monte Carlo method. Through empirical studies and case studies, this paper demonstrates the practical applications of these methods and discuss in depth the importance of risk management and model validation. This study also explores future research directions, including the development of advanced pricing models and financial innovation in emerging markets. Through these efforts, this paper provides valuable insights and methods for research and practice in finance.