Derivative Pricing under Uncertain Market Conditions: An Integrated Stochastic Volatility and Jump Framework

Abstract

With the increase in uncertainty of the modern financial market, so too has the problem of derivative pricing risen. Traditionally, the Black-Scholes model has been a solid theoretical model. However, it relies on idealized assumptions such as constant volatility and continuous asset price movements. I In reality, financial markets do not always conform to this classical model; instead, they exhibit time-varying volatility, heavy-tailed return distributions, and sudden price changes. Therefore, the old derivative pricing models have obvious shortcomings. This paper introduces an integrated framework for derivative pricing under uncertain market conditions. By adding stochastic volatility and jump risks to the model, it better reflects fluctuations in asset prices than a traditional diffusion model. Based on the above analysis, the value of derivatives is closely linked to the distribution of future asset prices, and this distribution is determined by expected returns, fluctuations in volatility and tail risks. This framework contributes to existing derivative pricing literature by integrating two major sources of uncertainty that are often modeled separately. Furthermore, the model provides practical implications for risk management and derivative valuation, particularly during periods of growing market uncertainty.