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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 84-95.doi: 10.6040/j.issn.1671-9352.0.2024.405

• • 上一篇    

混合次分数Vasicek随机利率模型下的缺口期权定价

李丽,宋瑞丽*   

  1. 南京财经大学应用数学学院, 江苏 南京 210023
  • 发布日期:2026-09-30
  • 通讯作者: 宋瑞丽(1979— ),女,教授,博士,研究方向为随机过程与金融数学. E-mail:songrl2007@163.com
  • 作者简介:李丽(1998— ),女,硕士研究生,研究方向为金融数学. E-mail:aurora1231230@163.com*通信作者:宋瑞丽(1979— ),女,教授,博士,研究方向为随机过程与金融数学. E-mail:songrl2007@163.com

Gap option pricing under the mixed sub-fractional Vasicek stochastic rate model

LI Li, SONG Ruili*   

  1. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu, China
  • Published:2026-09-30

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摘要： 基于混合次分数布朗运动驱动的风险资产价格过程,结合Vasicek随机利率模型,建立混合次分数Vasicek随机利率模型。借助Duffie的仿射结构解思想,推导零息票债券的定价公式。利用Δ-对冲原理得到期权价格所满足的偏微分方程,通过变量替换求得缺口期权的定价公式。通过数值模拟分析Hurst指数H、标的资产初始价格S、缺口G、到期日T、股票波动率σ2和利率波动率σr2对期权价格的影响。结果表明,参数H、G和σr2的提高会降低期权价格,而S、T和σ2的提高则使期权价格上升,推广已有的缺口期权的研究结果。

关键词: 混合次分数布朗运动, 缺口期权定价, 零息票债券, Vasicek随机利率

Abstract: A mixed sub-fractional Vasicek stochastic interest rate model is established based on the risky asset price process driven by mixed sub-fractional Brownian motion combined with the Vasicek stochastic interest rate model. With the help of Duffies idea of affine structure solution, the pricing formula of zero-coupon bond is derived. The partial differential equation satisfied by the option price is obtained using the Δ-hedging principle, and finally, the pricing formula for gap options is solved through variable substitution. Numerical simulations analyze the effects of Hurst index H, initial underlying asset price S, gap G, maturity date T, stock volatility σ2, and interest rate volatility σr2 on option prices. The results show that the increase in H, G, and σr2 will reduce the option price, while the increase in the S, T, and σ2 will increase the option price, which extends the existing research results on gap options.

Key words: mixed sub-fractional Brownian motion, gap option pricing, zero-coupon bond, Vasicek stochastic interest rate

中图分类号: 

  • O211.6
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[1] 安翔,郭精军. 混合次分数跳扩散模型下回望期权的定价及模拟[J]. 《山东大学学报(理学版)》, 2022, 57(4): 100-110.
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