双随机波动率跳扩散模型下一类扩展幂期权定价

Pricing Extendible Power Options in a Double Stochastic Volatility Jump-Diffusion Model

摘要: 扩展期权赋予持有者在原到期日延长期权执行期的选择权，是应对市场不确定性的动态风险管控利器，其核心价值源于灵活性与风险缓释能力。本文在双Heston随机波动率跳扩散模型框架下，提出一类扩展幂式期权的定价范式：借助Feynman-Kac定理刻画多维仿射结构，运用特征函数与快速傅里叶变换(FFT)技术，推导出单期扩展幂期权的显式定价公式。数值实验比较了不同模型下的价格差异，并剖析均值回复速率、波动方差及相关系数等关键参数的边际效应。结果表明，扩展幂期权在保留幂型杠杆放大效应的同时，通过展期条款有效压低尾部风险，兼具“高收益潜力”与“稳健风控”双重优势，更能适应瞬息万变的市场环境。

Abstract: Extendible options grant holders the right to prolong the exercise period at the original maturity date, serving as a dynamic risk management instrument to address market uncertainty. The core value of Extendible options lies in inflexibility and risk mitigation capability. Within the framework of double Heston stochastic volatility jump-diffusion model, this paper proposes a pricing approach for a class of extendible power options. By employing the Feynman-Kac theorem to characterize the multi-dimensional affine structure and utilizing characteristic functions along with the Fast Fourier Transform (FFT) technique, an explicit pricing formula for single-period extendible power options is derived. Numerical experiments compare price discrepancies under different models and analyze the marginal effects of key parameters such as mean-reversion speed, volatility variance, and correlation coefficients. The results demonstrate that extendible power options retain the leverage amplification inherent in power-type payoffs while effectively reducing tail risk through the extension feature. This dual advantage of “high-return potential” and “robust risk control” makes them particularly suited to rapidly changing market environments.