Scholarlink

<p>Empirical evidence implies that stochastic volatility with jump models significantly impacts option prices. This paper investigates the valuation of European options under the 3/2 stochastic volatility-plus-jump model, offering a more realistic framework for evaluating options in stock markets. We develop a Partial Integro-Differential Equation (PIDE) to price options with stochastic volatility dynamics and illustrate how this equation overcomes the limitations of the Black–Scholes model. The pricing equation is derived using risk–neutral valuation and self–financing portfolio replication. The radial basis function of the partition of unity (RBF–PU) method is applied to approximate the solutions of the derived PIDEs. As expected, the approximated solutions improve slightly the Black–Scholes option prices near strike prices meanwhile the convergence behavior of the numerical results confirms the accuracy of the approximation method. The numerical experiments indicate that the valuation prices are reliable and capture important financial market features.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Efficient Numerical Method for Pricing Options Under Stochastic Volatility with Jump Model

  • 期刊论文

  • 发表日期：

    2025年6月12日

查看全文
  • Roja Javid-Jahromi,
  • Abolfazl Tari Marzabad,
  • Ali Safdari-Vaighani

摘要

Empirical evidence implies that stochastic volatility with jump models significantly impacts option prices. This paper investigates the valuation of European options under the 3/2 stochastic volatility-plus-jump model, offering a more realistic framework for evaluating options in stock markets. We develop a Partial Integro-Differential Equation (PIDE) to price options with stochastic volatility dynamics and illustrate how this equation overcomes the limitations of the Black–Scholes model. The pricing equation is derived using risk–neutral valuation and self–financing portfolio replication. The radial basis function of the partition of unity (RBF–PU) method is applied to approximate the solutions of the derived PIDEs. As expected, the approximated solutions improve slightly the Black–Scholes option prices near strike prices meanwhile the convergence behavior of the numerical results confirms the accuracy of the approximation method. The numerical experiments indicate that the valuation prices are reliable and capture important financial market features.