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Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (7): 826-835.

• 论文 • 上一篇    下一篇

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

闫海峰1,2, 刘三阳1   

  1. 1. Department of Applied Mathematics, Xidian University, Xi’an 710071, P.R. China;
    2. Department of Mathematics, Henan Normal University, Xinxiang, Henan 453002, P.R.China
  • 收稿日期:2001-01-16 修回日期:2003-03-13 出版日期:2003-07-18 发布日期:2003-07-18
  • 通讯作者: YUN Tian-quan,Original Member of Editional Committee,AMM
  • 基金资助:
    the National Natural Science Foundation of China (69972036);the Natural Science Foundation of Henan Education Committee (1999110010)

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

YAN Hai-feng1,2, LIU San-yang 1   

  1. 1. Department of Applied Mathematics, Xidian University, Xi’an 710071, P.R. China;
    2. Department of Mathematics, Henan Normal University, Xinxiang, Henan 453002, P.R.China
  • Received:2001-01-16 Revised:2003-03-13 Online:2003-07-18 Published:2003-07-18
  • Supported by:
    the National Natural Science Foundation of China (69972036);the Natural Science Foundation of Henan Education Committee (1999110010)

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摘要： Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black-Scholes model is generalized to the case where the risk-less asset (bond or bank account) earns a time-dependent interest rate and risk asset (stock) has time-dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put-call parity of European option are obtained. The general approach of option pricing is given for the general Black-Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback (O-U) process are given by actuarial approach.

Abstract: Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black-Scholes model is generalized to the case where the risk-less asset (bond or bank account) earns a time-dependent interest rate and risk asset (stock) has time-dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put-call parity of European option are obtained. The general approach of option pricing is given for the general Black-Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback (O-U) process are given by actuarial approach.

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