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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (9): 46-54.doi: 10.6040/j.issn.1671-9352.0.2020.584

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混合分形Heston-CIR模型下的美式期权定价及模拟

郭精军,汪育兵,白亚楠*   

  1. 兰州财经大学统计学院, 甘肃 兰州 730020
  • 发布日期:2022-09-15
  • 作者简介:郭精军(1976— ),男,博士,教授,博士生导师,研究方向为金融统计与风险管理. E-mail:guojj@lzufe.edu.cn*通信作者简介:白亚楠(1994— ),女,硕士研究生,研究方向为金融统计与风险管理. E-mail:mynbai@126.com
  • 基金资助:
    国家自然科学基金资助项目(71961013);兰州财经大学科研创新团队支持计划(2020-02);甘肃省教育厅“双一流”科研重点项目(GSSYLXM-06)

American option pricing and simulation under the mixed fractional Heston-CIR model

GUO Jing-jun, WANG Yu-bing, BAI Ya-nan*   

  1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China
  • Published:2022-09-15

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摘要： 为了刻画标的资产呈现出的“波动率微笑”和“长相依”等特性,基于分形市场理论用标准布朗运动和分数布朗运动(H∈(3/4,1))的线性组合代替布朗运动,构建了混合分形Heston-CIR模型来描述标的资产价格。其次,讨论了该模型下随机微分方程的解的存在唯一性,并研究了利率方程的Euler格式离散化的强收敛性。最后,用最小二乘Monte Carlo算法对美式看跌期权进行数值模拟验证模型的有效性。

关键词: 美式看跌期权, 混合分形布朗运动, Heston-CIR模型, 最小二乘Monte Carlo算法

Abstract: In order to describe the volatility smile and long dependence of the underlying asset, a mixed fractional Heston-CIR model is constructed to describe the underlying asset price based on the fractional market theory,which replaces the Brownian motion with the linear combination of standard and fractional Brownian motion (H∈(3/4,1)). Secondly, the existence and uniqueness of solutions of stochastic differential equations under this model are discussed as well as the strong convergence of the Eolagian discretization of interest rate equation. Finally, the least-square Monte Carlo algorithm is used to simulate the American option to verify the validity of the model.

Key words: American put option, mixed fractional Brownian motion, Heston-CIR model, least-squares Monte Carlo algorithm

中图分类号: 

  • F224.7
[1] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3):637-654.
[2] FALLAH S, NAJAFI A R, MEHRDOUST F. A fractional version of the Cox-Ingersoll-Ross interest rate model and pricing double barrier option with Hurst index[J]. Communication in Statistics Theory and Methods, 2019(48):1-16.
[3] ROGERS L C G. Arbitrage with fractional Brownian motion[J]. Mathematical Finance, 1997, 7(1):95-105.
[4] CHERIDITO P. Mixed fractional Brownian motion[J]. Bernoulli Society for Mathematical Statistics and Probability, 2001, 7(6):913-934.
[5] MEHRDOUST F, NAJAFI A R, FALLAH S, et al. Mixed fractional Heston model and the pricing of American options[J]. Journal of Computational and Applied Mathematics, 2018(330):141-154.
[6] ZHANG Weiguo, LI Zhe, LIU Yongjun. Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion[J]. Statistical Mechanics and its Applications, 2018(490):402-418.
[7] 郭精军, 程志勇. 混合高斯模型下带红利的永久美式期权定价[J]. 应用数学, 2018, 31(2):250-256. GUO Jingjun, CHENG Zhiyong. Peppetual American pricing option in the mixed Gaussian model with dividend[J]. Mathematica Applicata, 2018, 31(2):250-256.
[8] HESTON S L. A closed-form solution for options with stochastic volatility with applications to bond and currency option[J]. Review of Financial Studies, 1993, 6(2):327-343.
[9] SAMIMI O, MEHRDOUST F. Pricing multi-asset American option under Heston stochastic volatility model[J]. International Journal of Financial Engineering, 2018, 3(5):1-16.
[10] MEHRDOUST F, BABAEI S, FALLAH S. Efficient Monte Carlo option pricing under CEV model[J]. Communications in Statistics Simulation and Computation, 2015, 46(3):2254-2266.
[11] AHLIP R, PARK L A F, PRODAN A. Pricing currency options in the Heston/CIR double exponential jump-diffusion model[J]. International Journal of Financial Engineering, 2017, 4(1):1-27.
[12] SAMIMI O, MARDANI Z, SHARAFPOUR S, et al. LSM algorithm for pricing American option under Heston-Hull-Whites stochastic volatility model[J]. Computational Economics, 2017(50):173-187.
[13] LONGSTAF F A, SCHWARTZ E S. Valuing American options by simulation:a simple least-squares approach[J]. Review of Financial Studies, 2001, 14(1):113-147.
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