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简化自融资条件下的蒙特卡罗期权定价方法研究

董纪昌,李泽西,董志,李秀婷   

  1. 中国科学院大学创新创业学院,   北京 100190
  • 出版日期:2018-04-25 发布日期:2021-06-25

董纪昌, 李泽西, 董志, 李秀婷. 简化自融资条件下的蒙特卡罗期权定价方法研究[J]. 系统科学与数学, 2021, 41(4): 953-966.

DONG Jichang, LI Zexi, DONG Zhi, LI Xiuting. Monte Carlo Option Pricing Under Simplified Self-Financing Condition[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 953-966.

Monte Carlo Option Pricing Under Simplified Self-Financing Condition

DONG Jichang, LI Zexi, DONG Zhi, LI Xiuting   

  1. School of Innovation and Entrepreneurship, University of Chinese Academy of Sciences, Beijing 100190
  • Online:2018-04-25 Published:2021-06-25
提出整合多种资产收益率波动特点且适用范围相对 较宽的期权定价模型进行期权的定价、校准和对冲.文章首先构建了 一类对数资产价格过程, 能够描述对数收益率的跳跃、非对称波动率 聚集、序列相关性和厚尾分布. 文章在简化的自融资条件下用蒙特卡罗 方法得到欧式看涨期权价格的近似解, 该方法同样适用于定价仅在到期日 支付的奇异期权. 在实证环节, 以对数收益率服从AR-FIEGARCH过程为例, 根 据上述定价模型提出校准上证50ETF期权和计算隐含波动率、Delta、Vega的 方法, 用期权组合进行Delta对冲和Delta-Vega对冲. 实验结果表明, 这两种 对冲方式均能有效降低投资组合价值波动. 因此, 所提出的定价模型和对冲 方法具有一定的实际意义和实用价值.
This article aims to propose an option pricing model which has strong model adaptability and can integrate a wide range of asset return characteristics. Under simplified self-financing condition, this article gets the approximate solution of option price through Monte Carlo simulation, which can also be applied to pricing exotic options with only expiration-day payment. This article also proposes a class of asset price process that can capture jump, asymmetric volatiltiy clustering, long-range dependence and fat-tail distribution in logarithmtic returns. In the empirical study, daily logarithmic return of SSE 50ETF is set to follow AR($n$)-FIEGARCH($p, d, q$) process. This article explains how to calibrate the implied volatility of SSE 50ETF option and calculats Delta and Vega. Experimental results show that the Delta hedging and Delta-Vega hedging can effectively reduce portfolio return volatility. Therefore, the pricing model and hedging method proposed in this article have practical value.
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