华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (2): 1-9.

• 应用数学与基础数学 •    下一篇

不变方差弹性三值期权定价

彭 斌1, 彭 菲2   

  1. 1. 中国人民大学 商学院, 北京 100872; 2. 大不列颠哥伦比亚大学 电子计算机学院, 温哥华 V6T 1Z4, 加拿大
  • 收稿日期:2010-04-01 修回日期:2010-07-01 出版日期:2011-03-25 发布日期:2011-03-25
  • 通讯作者: 彭斌

Pricing the constant elasticity of variance trinary option

PENG Bin1, PENG Fei2   

  1. 1. School of Business, Renmin University, Beijing 100872, China 2. Electrical & Computer Engineering, UBC, Vancouver, B.C. V6T 1Z4, Canada
  • Received:2010-04-01 Revised:2010-07-01 Online:2011-03-25 Published:2011-03-25
  • Contact: PENG Bin

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摘要： 不变方差弹性(CEV)模型可以阻止Black-Scholes模型中波动率微笑的实证偏差. 为此, 用CEV模型描述标的资产价格运动, 并按照非中心χ2分布余函数导出了三值期权的解析定价公式. 在此基础上, 提出了一 种计算非中心χ2分布余函数的简单有效算法. 指出当计算精确解有问题时, 提供该分布余函数近似值可以精确估计上述导出解析定价公式的结果. 该研究结果可以 推广到依赖时间参数的不变方差弹性奇异期权定价.

关键词: 不变方差弹性, 非中心χ2分布, 三值期权定价, 余函数, 不变方差弹性, 非中心χ2分布, 三值期权定价, 余函数

Abstract: The constant elasticity of variance (CEV) model can prevent the empirical bias exhibited by the Black-Scholes model such as the volatility smile. In this article, CEV model was used to describe the underlying asset price dynamics. The analytical pricing formula for the trinary option was derived in terms of complementary noncentral chi-square distribution function. A simply and efficient algorithm for computing this complementary distribution function was presented. Approximation to this complementary distribution function was provided to estimate accurately the result of the pricing formula derived above when the computation of the exact solution is problematic. This study will pave a new way to evaluate the class of the exotic option in the time dependent constant elasticity of variance.

Key words: noncentral chi-square distribution, trinary option, complementary function, constant elasticity of variance, noncentral chi-square distribution, trinary option, complementary function

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