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<p>Modeling the price of underlying asset for a financial derivative, requires careful consideration of various aspects of its stochastic behaviour. This paper focuses on three primary influential factors: stochastic volatility, stochastic liquidity and sudden spikes in the price of stock. Our model incorporates stochastic volatility using a Cox-Ingersoll-Ross stochastic differential equation, in line with the approach adapted in the Heston model. As a relatively underexplored yet significant factor in asset pricing, we model stochastic liquidity using an Ornstein-Uhlenbeck process. Furthermore, the model integrates jump components into the price dynamics to effectively capture substantial upward and downward fluctuotions that occur during periods of extraordinary market conditions. We derive an analytical solution for pricing European options and compare its results with real market observations, utilizing the Black-Scholes model as a benchmark. Finally, we include a brief sensitivity analysis to offer a more comprehensive overview of the introduced model. To ensure the robustness of our findings, we conduct the sensitivity analysis under three distinct regimes: baseline, volatile, and tranquil.</p>

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A Heston model with jumps and stochastic liquidity risk in European option pricing

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Parsa Yahyavi,
  • Navideh Modarresi

摘要

Modeling the price of underlying asset for a financial derivative, requires careful consideration of various aspects of its stochastic behaviour. This paper focuses on three primary influential factors: stochastic volatility, stochastic liquidity and sudden spikes in the price of stock. Our model incorporates stochastic volatility using a Cox-Ingersoll-Ross stochastic differential equation, in line with the approach adapted in the Heston model. As a relatively underexplored yet significant factor in asset pricing, we model stochastic liquidity using an Ornstein-Uhlenbeck process. Furthermore, the model integrates jump components into the price dynamics to effectively capture substantial upward and downward fluctuotions that occur during periods of extraordinary market conditions. We derive an analytical solution for pricing European options and compare its results with real market observations, utilizing the Black-Scholes model as a benchmark. Finally, we include a brief sensitivity analysis to offer a more comprehensive overview of the introduced model. To ensure the robustness of our findings, we conduct the sensitivity analysis under three distinct regimes: baseline, volatile, and tranquil.