广义Black-Scholes模型期权定价新方法——保险精算方法

闫海峰; 刘三阳

广义Black-Scholes模型期权定价新方法——保险精算方法

闫海峰^1,2,
刘三阳¹

1.
西安电子科技大学应用数学系, 西安 710071;
2.
河南师范大学数学与信息科学学院, 新乡 453002

基金项目: 国家自然科学基金资助项目(69972036);河南省教委自然科学基金资助项目(1999110010)

详细信息

作者简介:
闫海峰(1964- ),男,河南卢氏人,副教授,博士(E-mail:yhaif@263.net).

中图分类号: O211.6;F830.9
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- 文章访问数: 2347
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- 被引次数: 0
出版历程
- 收稿日期: 2002-01-16
- 修回日期: 2003-03-13
- 刊出日期: 2003-07-15

New Method to Option Pricing for the General Black-Scholes Model-An Acturarial Approach

YAN Hai-feng^1,2,
LIU San-yang¹

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

摘要

摘要: 利用公平保费原则和价格过程的实际概率测度推广了Mogens Bladt和Tina Hviid Rydberg的结果.在无中间红利和有中间红利两种情况下,把Black-Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况,在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系.给出了风险资产(股票)具有随机连续复利预期收益率和随机波动率的广义Black-Scholes模型的期权定价的一般方法.利用保险精算方法给出了股票价格遵循广义Ornstein-Uhlenback过程模型的欧式期权的精确定价公式和买权和卖权之间的平价关系.
- 期权定价 /
- Black-Scholes模型 /
- 公平保费 /
- O-U过程
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 riskless asset(bond or bank account) earns a time-dependent interest rate and risky 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) with a stochastic 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 process are given by actuarial approach.
- option pricing /
- Black-Scholes model /
- fair premium /
- O-U process

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参考文献(10)

[1]	Merton R.Optimum consumption and portfolio rules in continuous time model[J].Journal of Economic Theory,1971,3(3):373-413.
[2]	Black F,Scholes M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973,81(4):633-654.
[3]	Duffie D.Security Markets:Stochastic Models[M].Boston:Academic Press,1988.
[4]	Bladt M,Rydberg H T.An actuarial approach to option pricing under the physical measure and without market assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.
[5]	Duffie D.Dynamic Asset Pricing Theory[M].Princeton,New Jersey:Princeton University Press,1996.
[6]	Merton R.Continuous-Time Finance[M].Oxford:Blacwell Publishers,1990.
[7]	Kouritzin M A,Deli Li.On explicit solution to stochastic differential equation[J].Stochastic Analysis and Applications,2000,18(4):571-580.
[8]	薛宏.鞅方法在未定权益定价中的应用[J].工程数学学报,2000,17(1):135-138.
[9]	Roos Cox J C,Rubinstein S A.Option pricing:A simplified approach[J].Journal of Economics,1979,7(2):229-263.
[10]	Bernt,Фksendal.Stochasitc Differential Equations[M].Fourth Ed.New York:Springer-Verlag,1995.